Mathematics, 07.04.2020 17:27 hectorgonzalejr333

A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission. The following is the setup for the hypothesis test: H0:p=0.10 Ha:p<0.10 In this example, the p-value was determined to be 0.299. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim.

Answers: 1

Show answers

Answers

Answer from: ld966057

The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim.

Step-by-step explanation:

A one-proportion z-test can be used to determine whether the proportion of cars with manual transmission is less than 10%.

The hypothesis is defined as:

H₀: The proportion of cars with manual transmission is 10%, i.e. p = 0.10.

Hₐ: The proportion of cars with manual transmission is less than 10%, i.e. p < 0.10.

The information provided is:

$X=95\\n=1000\\\alpha =0.05\\p-value=0.299$

The test statistic is:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$

Decision rule:

If the p-value of the test is less than the significance level (α) then the null hypothesis will be rejected or else accepted.

The p-value = 0.299 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.

Conclusion:

As the null hypothesis was not rejected it can be concluded that the proportion of cars with manual transmission is 10%.

Thus, the correct option is:

"The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim."

Answer from: CoreyHammond584

The calculated value Z = 22.22 > 1.96 at 5% level of significance

Therefore the null hypothesis is rejected.

The conclusion is that there is not enough evidence to support the claim

Step-by-step explanation:

Step 1:-

A researcher claims that the proportion of cars with manual transmission is less than 10%.

P = 10% = 0.10

Given sample size n= 1000

given the Sample proportion is p = 0.299

Null hypothesis: H₀: P =0.10

Alternative hypothesis :Ha:p<0.10

Level of significance α=0.05

Step 2:-

The test of hypothesis $Z = \frac{p-P}{\sqrt{\frac{PQ}{n } } }$

put all values , we get

$Z = \frac{0.299-0.10}{\sqrt{\frac{0.10X0.90}{1000 } } }$

on calculation , we get

$Z = \frac{0.199}{0.0094} = 22.22$

The 5 % level of significance of tabulated value = 1.96

Conclusion:-

The calculated value Z = 22.22 > 1.96 at 5% level of significance

Therefore the null hypothesis is rejected.

The conclusion is that there is not enough evidence to support the claim

Answer from: Quest

29. because you will divide each number of months by 12 to find the number of years. which would mean, 5, 12.5, 16, 45, 50, 72.5. which is crazy. anyhow, i think you find the median in the middle. and yea hope your test goes good

Answer from: Quest

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:50, winterblanco

Which of the following is the equation that says that the product of a number and ten is equal to 20 percent of that number ? a) 10n= 2.0n b) 10+n=.20n c) n+ .20n=10 d) 10n=0.20n

Answers: 1

continue

Mathematics, 22.06.2019 01:30, nickeymcorrea

The pyraminx is a rubik's cube-type toy in the shape of a tetrahedron. the pyraminx shown below has edges 15\,\text{cm}15cm long and vertical height h=12.2\,\text{cm}h=12.2cm. the triangle drawn with dashed lines is a right triangle. what is the distance rr? round your answer to the nearest tenth.

Answers: 1

continue

Mathematics, 22.06.2019 02:10, christinasmith9633

Which diagram best shows how fraction bars can be used to evaluate 1/2 divided by 1/4?

Answers: 2

continue

Mathematics, 22.06.2019 03:50, jescanarias22

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.

Answers: 3

continue

You know the right answer?

A researcher claims that the proportion of cars with manual transmission is less than 10%. To test t...