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Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate. Round your answer to the nearest thousandth. n1 = 677 n2 = 3377
x1 = 172 x2 = 654

Answers

Answer 1

Answer:

Answer:

The calculated value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Step-by-step explanation:

Given first sample size n₁ = 677

First sample proportion

$p^(-) _(1) = (x_(1) )/(n_(1) ) = (172)/(677) = 0.254$

Given second sample size n₂ = 3377

second sample proportion

$p^(-) _(2) = (x_(2) )/(n_(2) ) = (654)/(3377) = 0.1936$

Null Hypothesis : H₀ : p₁ = p₂.

Alternative Hypothesis : H₁ : p₁ ≠ p₂.

Test statistic

$Z = \frac{p_(1) ^(-)-p^(-) _(2) }{\sqrt{P Q((1)/(n_(1) ) +(1)/(n_(2) )) } }$

where

$P = (n_(1) p_(1) + n_(2) p_(2) )/(n_(1)+n_(2) ) = (677 X 0.254+3377 X 0.1936)/(677+3377)$

P = 0.2036

Q = 1 - P = 1 - 0.2036 = 0.7964

$Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964((1)/(677 ) +(1)/(3377 )) } }$

Z = 3.775

Critical value ∝=0.05

Z- value = 1.96

The calculated value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Related Questions

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Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
7n+4n combine the like terms to create an equivalent expression

5.
X
1 1 2 2 3 3 4
FX) -1 3 4 0 5 1 6
Label:
Explanation:

Answers

Answer:

Not a function

Step-by-step explanation:

Each input can have only have one output.

x(1) can't equal both -1 and 3 at the same time.

x(2) can't equal both 4 and 0 at the same time.

x(3) can't equal both 5 and 1 at the same time.

In other words there can't be multiple X's equalling different things.

PLEASEE HELPPPP PLEASEE thiss IS FOR MY FRIEND I BEGG YOUUU PLEASEEE

Answers

Answer:

Step-by-step explanation:

Why are you asking? Why isn't your friend?

The diagram assumes that the angle on the lower left of the triangle is a right angle. If it is not, then I don't think there is a way that this can be solved.

Tan(A) = opposite / adjacent

opposite = 7

Adjacent = 4

Tan(A) = 7/4 = 1.75

A = inverseTan (1.75)

A = 60.60 degrees

A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.20
-16
12
-8
-20 -16 -12
-
-4
48
12
16 2024
-8
-12
16
If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

Answers

I don’t any idea for this

On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?

Answers

Answer:

The test statistic is -2.5

Yes, I can reject the null hypothesis at 5% significance level.

Step-by-step explanation:

Null hypothesis: The average number of sardines in a can is 9.75

Alternate hypothesis: The average number of sardines in a can is greater than 9.75

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 9.75

population mean = 10

sd = 1

n = 100

z = (9.75 - 10) ÷ 1/√100 = -0.25 ÷ 0.1 = -2.5

The test is a one-tailed test. At 5% significance level, the critical value is 1.645

Conclusion:

Reject the null hypothesis because the test statistic -2.5 is less than the critical value 1.645

Rewrite each fraction with a denominator of 121212.
\dfrac{3}{4} =

Answers

Answer:

9/12

Step-by-step explanation:

First you multiply 3x12 which equal 36 then you divide 36 by 4 which equal 9 so your answer is 9/12

Assume a significance level ofα=0.05

and use the given information to complete parts (a) and (b) below.Original claim:

LessLess

than

51%

of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of

0.0148

a. State a conclusion about the null hypothesis. (Reject

Upper H 0H0

or fail to reject

Upper H 0H0.)

Choose the correct answer below.

A.

RejectReject

Upper H 0H0

because the P-value is

less than or equal toless than or equal to

alphaα.

B.

RejectReject

Upper H 0H0

because the P-value is

greater thangreater than

alphaα.

C.

Fail to rejectFail to reject

Upper H 0H0

because the P-value is

greater thangreater than

alphaα.

D.

Fail to rejectFail to reject

Upper H 0H0

because the P-value is

less than or equal toless than or equal to

alphaα.

b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?

A.

The percentage of adults that would erase all of their personal information online if they could is

lessless

than or equal to

51%.

B.

There

isis

sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

C.

The percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

D.

There

is notis not

sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

Answers

Answer:

Part a: The correct answer is A, reject H0 because p value is less than $\alpha$ . Part B: The correct answer is C, the percentage of adults that would erase their personal information online if they could is more than 51%.

Step-by-step explanation:

part a. The essential idea of hypothesis testing in statistics is to evaluate the probability p (p value) of some representative parameter, compared to a level of likelihood that is set before starting the test ( $\alpha$ ). In this case, we are interested in a level of likelihood $\alpha=0.05$ , which means that if the probability of the parameter is less than 5%, we will reject the hypothesis that this parameter is representing, since it's so unlikely. Of course, the significance level is arbitrary and must be payed attention, according to the particular situation. Therefore, the correct anser is A.

part b. Since we rejected the hypothesis to a 5% significance level, we reject the fact that less than 51% of adults would erase their personal information online if they could. This is equivalent to saying that a percentage of adults equal to or more than 51% would erase their personal information if they could, which is answer C.

Final answer:

We should reject the null hypothesis because the P-value is less than the significance level. This provides statistically significant evidence to support the claim that less than 51% of adults would erase all of their personal information online if they could.

Explanation:

The questions relate to hypothesis testing in Statistics, which is a tool to make inferences about a population parameter based on a sample's observation.

a. In hypothesis testing, a P-value is the probability that the observed data would occur under the null hypothesis. If the P-value is less than or equal to the significance level α, we reject the null hypothesis. In this case, the P-value is 0.0148, which is less than the significance level α=0.05. Therefore, we should Reject the null hypothesis. The correct answer is A.

b. Since we rejected the null hypothesis, we have evidence to support the alternate hypothesis. In this context, the original claim was that less than 51% of adults would erase all of their personal information online if they could. The test result provides statistically significant evidence to support the original claim. Therefore, the correct conclusion is A.