Question

in a survey of 1000 adult americans, 44.5% indicated that they were somewhat interested or very interested in having web access in their cars. suppose that the marketing manager of a car manufacturer claims that the 44.5% is based only on a sample and that 44.5% is close to half, so there is no reason to believe that the proportion of all adult americans who want car web access is less than 0.50. is the marketing manager correct in his claim? provide statistical evidence to support your answer. for purposes of this exercise, assume that the sample can be considered as representative of adult americans. test the relevant hypotheses using

Answer 1

Answer: No, the marketing manager was not correct in his claim.

We are given that in a survey of 1005 adult Americans, 46.6% indicated that they were somewhat interested or very interested in having web access in their cars.

Suppose that the marketing manager of a car manufacturer claims that the 46.6% is based only on a sample and that 46.6% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50.

Let p = population proportion of all adult Americans who want car web access.

SO, Null Hypothesis, : p 50% {means that the proportion of all adult Americans who want car web access is more than or equal to 0.50}

Alternate Hypothesis, : p < 50% {means that the proportion of all adult Americans who want car web access is less than 0.50}

The test statistics that will be used here are One-sample z-proportion statistics;

T.S. = ~ N(0,1)

where = sample proportion of Americans who indicated that they were somewhat interested or very interested in having web access in their cars = 46.6%

n = sample of Americans = 1005

So, test statistics =

= -2.161

Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives the critical value of -1.6449 for the left-tailed test. Since our test statistics are less than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Explanation:

Answer 2

To test the marketing manager's claim, we conduct a hypothesis test using a one-tailed z-test. The test results suggest that the marketing manager is incorrect in claiming that the proportion of all adult Americans who want car web access is not less than 0.50.

To determine whether the marketing manager is correct in claiming that the proportion of all adult Americans who want car web access is not less than 0.50, we need to conduct a hypothesis test.

The null hypothesis is that the proportion is 0.50, and the alternative hypothesis is that the proportion is less than 0.50.

We can use a one-tailed z-test to test the hypotheses. Using the given information that 44.5% of the sample size of 1000 adult Americans indicated interest in car web access, we can calculate the test statistic and the p-value.

If the p-value is less than the chosen significance level (usually 0.05), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Based on the calculations, the test statistic will be positive, and the p-value will be less than 0.05. Therefore, we can reject the null hypothesis and conclude that there is evidence to suggest that the proportion of all adult Americans who want car web access is less than 0.50, contradicting the marketing manager's claim.