Answer:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=60[/tex] represent the sample mean
[tex]s=22[/tex] represent the sample standard deviation
[tex]n=400[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean for this case is higher than 40 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 36 modified components produce a mean time between failures of 960 hours, with a standard deviation of 52 hours. Using a significance level of .01, test the claim that, for modified components, the mean time between failures is greater than 937 hours. Find the appropriate p-value.
Answer:
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Test Statistics z = 2.65
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
P- value = 0.004025
Step-by-step explanation:
Given that:
Mean [tex]\overline x[/tex] = 960 hours
Sample size n = 36
Mean population [tex]\mu =[/tex] 937
Standard deviation [tex]\sigma[/tex] = 52
Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours
Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]
Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]
Degree of freedom = n-1
Degree of freedom = 36-1
Degree of freedom = 35
The level of significance ∝ = 0.01
SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;
from t-table t(0.99,35), the critical value = 2.438
The test statistics is :
[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}[/tex]
[tex]Z = \dfrac{23}{8.66}[/tex]
Z = 2.65
The decision rule is to reject null hypothesis if test statistics is greater than critical value.
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
The P-value can be calculated as follows:
find P(z < - 2.65) from normal distribution tables
= 1 - P (z ≤ 2.65)
= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))
= 0.004025
factoriza C (x) 42x4 − 36x2 + 24x + 12
Answer:
factor out 12
[tex]12(14cx - 5 + 2x)[/tex]
C. One half of the sum of six times a number and twenty-two
Answer:
Step-by-step explanation:
One half
The improper fraction 37/6 can be changed to the mixed number
Answer: 6 1/6
Step-by-step explanation:
6 can go into 37 6 times
6x6=36
with 1 left over
The fraction 37/6 can be changed to the mixed number as 6 1/6 if the fraction is 37/6.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fraction is:
= 37/6
We can write the above number as:
= (36 + 1)/6
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 36/6 + 1/6
= 6 + 1/6
Or
= 6 1/6 (mixed fraction)
Thus, the fraction 37/6 can be changed to the mixed number as 6 1/6 if the fraction is 37/6.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
Suppose a certain item used to sell for 30 cents per pound, and you see that it’s been marked up to 45 cents per pound. What is the percent increase?
Answer:
50%
Step-by-step explanation:
45 cents is 15 cents more than 30 cents. The increase in cents is 15.
15 is half of 30. Half is also 0.5, 1/2, or 50%. The increase is 50%.
You can also answer this using the percent change formula.
percent change = (new number - old number)/(old number) * 100%
percent change = (45 - 30)/30 * 100%
percent change = 15/30 * 100%
percent change = 0.5 * 100%
percent change = 50%
If the result is positive, it is a percent increase.
If the result is negative, it is a percent decrease.
Find the volume. Round your answer to one decimal place.
(PLZ SOMEBODY HELP ASAP)
Answer:
32.738ft³
32.7ft³
Step-by-step explanation:
This is half a sphere therefore volume=4/3πr³×1/2
4/3×22/7×2.5³×1/2
=32.738ft³
What are the factors of the expression below 9x^2+6x+1?
[tex]answer = (3x + 1)\\ solution \\ {9x}^{2} + 6x + 1 \\ = {9x}^{2} + (3 + 3)x + 1 \\ = {9x}^{2} + 3x + 3x + 1 \\ = 3x(3x + 1) + 1(3x + 1) \\ = (3x + 1)(3x + 1) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Factor the trinomial completely
8a^2+65ab+8b^2
a trapazoid is a quadrilateral with one or more pairs of paralllel sides true or false
yes the answer is( true).
Answer:
The answer is (True)
Step-by-step explanation:
The sets F and H are given below.
F={c,f,g}
H= {d,e,h)
Find the union of F and H.
Find the intersection of F and H.
Answer:
F ∪ H = {c, d, e, f, g, h}
F ∩ H = { }
Step-by-step explanation:
The union is the list of elements that are in either of the two sets.
F ∪ H = {c, d, e, f, g, h}
The intersection is the list of only those elements that appear in both sets. (There are none.)
F ∩ H = { } . . . . the empty set
A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist. What is the expected revenue of the tour operator?
Answer:
The expected revenue is $984.6.
Step-by-step explanation:
The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.
The tourist have a probability of 0.02 of not showing up, independent of each other.
The income is the selling of the 21 tickets at $50 each.
[tex]I=21*50=1,050[/tex]
The only cost considered in this problem is the refund if a tourist show up and a seat is not available.
This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.
For the event that the 21 tourists show up, we have the probability:
[tex]P=0.98^{21}\approx0.654[/tex]
For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:
[tex]E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6[/tex]
Q 3.28: To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail. Indicate what percent of values must be chopped off from each tail for a 97% confidence level. A : We keep the middle 97% of values by chopping off 1.5% from each tail. B : We keep the middle 1.5% of values by chopping off 97% from each tail. C : We keep the middle 3% of values by chopping off 97% from each tail. D : We keep the middle 3% of values by chopping off 1.5% from each tail. E : We keep the middle 97% of values by chopping off 3% from each tail.
Answer:
A : We keep the middle 97% of values by chopping off 1.5% from each tail.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.97}{2} = 0.015[/tex]
This means that for a 97% confidence interval, 1.5% of each tail is removed, while the middle 97% of values are kept.
So the corect answer is:
A : We keep the middle 97% of values by chopping off 1.5% from each tail.
I NEED HELP!!! NOW!!!! A shape is picked at random from the group below.
2 circles, 4 triangles, and 2 squares.
Which event has a theoretical probability of exactly Three-fourths? Select three options.
not picking a square
picking a square
picking a triangle
picking a shape that has only straight edges
not picking a circle
Theoretical probability formula: Favorable Outcomes/All Possible Outcomes
So let's find the theoretical probability for each option.
"Not picking a square"
So, there are 2 squares out of the 8 total shapes (2 circles + 4 triangles + 2 squares) So do 8-2=6... This is subtracting the number of squares out. So we are now left with 6/8.. Reduce the fraction: GCF is 2, so 6/8 simplifies to 3/4. So, "Not picking a square" is an option!
"Picking a square"
Okay so there are 2 squares (favorable outcome) out of 8 shapes in total (all possible outcomes) so the fraction is 2/8. Now simplify: GCF = 2, so 2/8 = 1/4. "Picking a square" is NOT an option
"Picking a triangle"
There are 4 triangles out of 8 shapes, so the fraction is 4/8 which = 1/2. The theoretical probability of picking a triangle is 1/2 and thus NOT an option.
"Picking a shape that has only straight edges"
So this basically means every shape that's not a circle. So, there are 4 triangles + 2 squares = 6 total shapes with straight edges. So there are 6 shapes with straight edges out of 8 total shapes: 6/8 reduces to 3/4. "Picking a shape that has only straight edges" IS an option! :D
LASTLY!
"Not picking a circle"
There are only 2 circles out of 8 total shapes, so 8-2=6 so the fraction is 6/8. This reduces to 3/4. "Not picking a circle" Is an option!
CORRECT ANSWERS:
Not picking a square
Picking a shape that has only straight edges
Not picking a circle
Have a good day!
Answer:
A, D, and E
Step-by-step explanation:
got it right on edge
The volume of gas V held at a constant temperature in a closed container varies inversely with its pressure P.If the volume of gas is 400 cubic centimeters (cc) . When The pressure is 300 millimeters of mercury ( mm Hg) , find the volume when the pressure is 500 mm Hg .
When the pressure is 500 mm Hg, the volume is
Answer:
240cc
Explanation:
From the expression of the relationship between pressure and volume, we can state mathematical that for two successive volume V1 and V2 and Pressure P1 and P2 we have:
P1V1 = P2V2
V2 = P1V1 / P2
=400×300/500= 240cc
A rectangular box with a volume of 684 ftcubed is to be constructed with a square base and top. The cost per square foot for the bottom is 20cents, for the top is 15cents, and for the sides is 1.5cents. What dimensions will minimize the cost?
Answer:
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost=2046.16 cents
Step-by-step explanation:
Given that a rectangular box with a volume of 684 ft³.
The base and the top of the rectangular box is square in shape
Let the length and width of the rectangular box be x.
[since the base is square in shape, length=width]
and the height of the rectangular box be h.
The volume of rectangular box is = Length ×width × height
=(x²h) ft³
[tex]x^2h=684\Rightarrow h=\frac{684}{x^2}[/tex] (1)
The area of the base and top of rectangular box is = x² ft²
The surface area of the sides= 2(length+width) height
=2(x+x)h
=4xh ft²
The total cost to construct the rectangular box is
=[(x²×20)+(x²×15)+(4xh×1.5)] cents
=(20x²+15x²+6xh) cents
=(25x²+6xh) cents
Total cost= C(x).
C(x) is in cents.
∴C(x)=25x²+6xh
Putting [tex]h=\frac{684}{x^2}[/tex]
[tex]C(x)=25x^2+6x\times\frac{684}{x^2} \Rightarrow C(x)=25x^2+\frac{4104}{x}[/tex]
Differentiating with respect to x
[tex]C'(x)=50x-\frac{4104}{x^2}[/tex]
To find minimum cost, we set C'(x)=0
[tex]\therefore50x-\frac{4104}{x^2}=0\\\Rightarrow50x=\frac{4104}{x^2}\\\Rightarrow x^3=\frac{4104}{50}\Rightarrow x\approx 4.345[/tex] ft.
Putting the value x in equation (1) we get
[tex]h=\frac{684}{(4.345)^2}[/tex]
≈36.23 ft.
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents
=2046.16 cents
00:00
Gavin counted the number of days until the end of school.
If he counted the days in groups of 7, which list shows the numbers Gavin could have
named?
O
A. 7, 15, 22, 30
B. 7, 14, 21, 30
C. 7, 14, 21, 28
D. 14, 21, 32, 38
Answer:
C. 7, 14, 21, 28
Step-by-step explanation:
Since you know your times tables, you know that multiples of 7 are ...
7, 14, 21, 28
A number is randomly selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10).
What is the COMPLEMENT of selecting a number greater than 7?
Enter your answer as a FRACTION.
In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is [tex]\boxed{\frac{7}{10}}.[/tex]
Answer:
it is 3/10
Step-by-step explanation:
1, 2, 3, 4, 5, and 6 are all LESS than 7. 8, 9, and 10 are all GREATER than 7, therefor, [tex]\frac{3}{10}[/tex] is the complement.what is the following quotient,
sqrt96/ sqrt8
Answer:
The answer is option 1.
Step-by-step explanation:
Firstly, you have to get rid of square root at the denorminator by multiply both side with √8 :
[tex] \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} [/tex]
[tex] \sqrt{a} \times \sqrt{a} = a[/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{96} \times \sqrt{8} }{ \sqrt{8} \times \sqrt{8} } [/tex]
[tex] \frac{ \sqrt{768} }{8} [/tex]
Next, you have to simply by looking which factor is a perfect square :
[tex] \frac{ \sqrt{256 \times 3} }{8} [/tex]
[tex] \frac{16 \sqrt{3} }{8} [/tex]
[tex]2 \sqrt{3} [/tex]
Answer:
its a
Step-by-step explanation:
on edge 2022
y - ( -3y ) what is the answer????
Answer:
4y
Step-by-step explanation:
y - -3y
Subtracting a negative is like adding
y+3y
Combine like terms
4y
Answer:
[tex]4y[/tex]
Step-by-step explanation:
[tex]y - ( - 3y) \\ y + 3y \\ = 4y[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
1, 2, 5, 10, 17, 26, 37, whats next
Answer:
50, 65, 82, 101,122,145,170.
Step-by-step explanation:
hope this helps
(Add two to an odd number and continue doing so)
example: 1+1 =2, 2+3 = 5, 5+5 = 10, 10+7 = 17, and so on so forth.
The radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)
How many times larger is the 15” than 10” pizza?
Is this surprising? Why or why not?
If you doubled the diameter of a circle, how many times larger would it’s area become?
Answer:
846^% and then to rond it is 850^%
Step-by-step explanation:
e radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)
Tomas has two boxes to be shipped. One box weighs 3 \text{ kilograms}3 kilograms3, start text, space, k, i, l, o, g, r, a, m, s, end text. The other box weighs 720 \text{ grams}720 grams720, start text, space, g, r, a, m, s, end text.
Answer:
3.72kg
$29.76
See explanation below
Step-by-step explanation:
The question is incomplete as we are not told what we are to determine. Consider the following question
Question:
Tomas has two boxes to be shipped. One box weighs 3 kilograms. The other box weighs 720 grams.
a) What is the total weight of the boxes in kilogram?
b) If the shipping cost $8 per kilogram, what is the total cost of shipping.
Solution:
This is a question on measuring mass.
a) Total weight of the two boxes = weight of 1st box + weight of 2nd box
1st box = 3kg
2nd box = 720g
1000 g is equal to 1 kg
720g = (720/1000)kg = 0.72 kg
2nd box = 0.72 kg
Total weight of the two boxes = 3kg + 0.72kg
Total weight of the two boxes = 3.72kg
b) cost of shipping per kg = $8
cost of shipping for 3.72 kg = 8 × 3.72
Total cost of shipping for both boxes = $29.76
Answer: from my calculations its 3.72
which is also 3720 grams
Cherry Trees: Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the Allegheny National Forest, Pennsylvania. Height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet. (Hand, 1994)Estimate Std. Error t value P(>|t|)(Intercept) -57.99 8.64 -6.71 0.00height 0.34 0.13 2.61 0.01diameter 4.71 0.26 17.82 (c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONEOnly diameter is a significant predictor since it has the smallest p-valueYes, since the p-values associated with each predictor are less than 0.05No, since the p-values associated with each predictor are less than 0.05(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________ cubic feet(e) A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONEoverestimateunderestimate
Answer:
(c) Yes, since the p-values associated with each predictor are less than 0.05
(d) 22.093 cubic feet
(e) underestimate
Step-by-step explanation:
Our main objective is to determine the following
(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONE Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
No, since the p-values associated with each predictor are less than 0.05
Assuming our significance level ∝ = 0.05
From the data given;
p-value for height is = 0.00
p - value for diameter = 0.01
where, p-value ( = 0.01 and 0.00 ) < ∝ (= 0.05 )
Hence, according to the rejection rule; the null hypothesis is rejected and the predictors "height" and " diameter" are significant predictors of volume.
Thus
The answer is :
Only diameter is a significant predictor since it has the smallest p-value
Yes, since the p-values associated with each predictor are less than 0.05
(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________
[tex]\hat y = -57.99+ 0.34 \ \mathbf{height }+4.71 \ \mathbf{diameter}[/tex]
[tex]\hat y = -57.99+ 0.34 \ \mathbf{(79)}+4.71 \ \mathbf{(11.3)}[/tex]
[tex]\hat y = 22.093 \ cubic foot[/tex]
(e)
A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONE
overestimate
underestimate
We can posits that the model gives an underestimate of the volume of this tree due to the fact that the predicted value is 22.093 and which is less than the observed value of 24.2 cubic feet.
On June 18, Smith Technologies issued a $75,000, 6%. 180-day note payable to Johnson Company. What is
the due date of the note? 15
a. December 16
b. December 17
Answer:
a. December 16
Step-by-step explanation:
18 June + 180 days = 15 December
Since 2 options given,
a. December 16 is the answer
The HR department of a large company wants to determine how often to bring representatives from the financial firm managing employee pensions on site to meet with individuals about their retirement plans. In order to determine level of interest, they decide to survey employees. Suppose they group employees by age categories (e.g., under 30; 30 – under 45; 45 – under 60, 60 or older) and randomly select 50 individuals from each category. This sampling plan is called ________________________ .
a) stratified samplingb) simple random samplingc) cluster samplingd) convenience samplinge) systematic sampling
Answer:
Systematic Sampling
Step-by-step explanation:
Y is directly proportional to (x+2)2 when x=8 y=250 find y when x=4
Answer:
Y=150
Step-by-step explanation:
Just apply the proportionality rulw and solve for k. Then substitute the value of k into the equation.
Answer:
90
Step-by-step explanation:
Let the constant of proportionality be K
So that;
Y= K(x+2)^2
This means
For two corresponding points (x1,y1) and (x2,y2) we have;
Y1/(x1+2)^2= Y2/(x2+2)^2
If we consider x=8 y=250 as point (x1,y1) and y when x=4 as (x2,y2) we have ;
250/(8+2)^2 =y/(4+2)^2
250/(10)^2 = y/(6)^2
250/100 = y/36
250/100 × 36 = y
90= y
y=90
Imagine that you are conducting a one-variable chi-square test to investigate the hypothesis that there are equal numbers of cat lovers and dog lovers in the office at work. Having conducted a survey, you found 150 preferred dogs and 120 preferred cats. What would the expected frequencies be in each cell? 135 150 and 120 270 More information is needed to calculate the expected frequencies.
Answer:
135
Step-by-step explanation:
Based on the following information:
- There are 150 dog lovers
- There are 120 cat lovers
So:
The null hypothesis:
H, there are an equal number of dog lovers and cat lovers, so the expected frequency in each cell will be the same and that is:
f = (150 + 120) / 2
f = 270/2 = 135
then the first option of 135 is correct
A bag contains four red, three green, and five yellow marbles. Three marbles are drawn,
One at time, without replacement. Determine the probability that the order in which they
are selected is(9A)
Ca) Yellow, red, green
(b) Yellow, green, green
(c) Yellow, Yellow, red
m how many ways can neople be selected from a group that consists of four adults a
Suppose a standard six-sided die is rolled and you receive $0.50 for every dot showing on the top of the die. What should the cost of playing the game be in order to make it a fair game?
The cost of playing the game should be $. ?
] It is claimed that 42% of US college graduates had a mentor in college. For a sample of college graduates in Colorado, it was found that 502 out of 1045 had a mentor in college. Test the claim that the proportion of college grads in Colorado who had a mentor is greater than that of all US college grads. Set up a sampling distribution of proportions.
Answer:
[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.930)=0.0000443[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42
Step-by-step explanation:
Information given
n=1045 represent the random sample selected
X=502 represent the college graduates with a mentor
[tex]\hat p=\frac{502}{1045}=0.480[/tex] estimated proportion of college graduates with a mentor
[tex]p_o=0.42[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true proportion is higher than 0.42, the system of hypothesis are.:
Null hypothesis:[tex]p \leq 0.42[/tex]
Alternative hypothesis:[tex]p > 0.42[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.930)=0.0000443[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42
