A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked

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2 months ago

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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.

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-03-25T15:53:48+03:00

zzz [12.3K]2 months ago

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The computed Z value is 22.22, which is greater than 1.96 at a 5% significance level. Consequently, the null hypothesis is rejected. This leads to the conclusion that there is insufficient evidence to validate the claim.

zzz [12.3K] · Answer 2 · 2026-03-25T15:54:30+03:00

The conclusion is to not reject the Null Hypothesis. This indicates insufficient evidence to affirm the claim. A one-proportion z-test assesses whether the proportion of cars with manual transmission is below 10%. The hypotheses are defined as: H₀: The proportion equals 10%, meaning p = 0.10; Hₐ: The proportion is less than 10%, so p < 0.10. The rules state that if the p-value is below the significance level (α), the null hypothesis is rejected; otherwise, it is retained. Here, the p-value is 0.299, which is greater than α = 0.05, resulting in a failure to reject the null hypothesis at a 5% significance level. Hence, it is concluded that the proportion of cars with manual transmission stands at 10%.