The average age of online consumers a few years ago was 21.1 years. As older individuals gain confidence with theInternet, it is believed that the average age has increased. We would like to test this belief. Answer partsa) throughe) below.

a) Write the appropriate hypotheses. Choose the correct answer below.

A.

H0: <24.8 years HA: =24.8 years

B.

H0: =24.8 years HA: >24.8 years

C.

H0: >24.8 years HA: =24.8 years

D.

H0: =24.8 years HA: <24.8 years

b) We plan to test the null hypothesis by selecting a random sample of 41 individuals who have made an online purchase this year. Do you think the necessary assumptions for inference aresatisfied? Explain. Choose the correct answer below.

A.

Yes. The Independence Assumption is met since the sample was selected randomly. The Nearly Normal Condition is met since the sample of 41 shoppers is likely large enough to be safe to proceed(given that there is not any outliers or serious skewness in thedistribution).

B.

No. The sample was not selectedrandom, which violates the Independence Assumption.

C.

Yes. More than10% of the sample was selectedrandomly, which satisfies the Independence Assumption.Furthermore, a sample of 41 shoppers is a sufficient sample size to satisfy the Nearly Normal Condition as long as serious skewness and outliers are not present in the distribution.

D.

No. The sample is not large enough to safely assume that the Nearly Normal Condition is satisfied.

c) The online shoppers in our sample had an average age of 22.2 years, with a standard deviation of 4.8 years.What's theP-value for thisresult?

TheP-value is

(Round to three decimal places asneeded.)

d) Explain(in context) what thisP-value means. Choose the correct answer below.

A.

The probability of a random sample of 41 shoppers having an age less than the hypothesized mean age is equal to theP-value.

B.

The probability of a random sample of 41 shoppers having an age more than the hypothesized mean age is equal to theP-value.

C.

If the mean age of shoppers remains at 24.8 years, the probability of getting a sample mean of 22.2 years or older simply from natural sampling variation is equal to theP-value.

D.

If the mean age of shoppers remains at 22.2 years, the probability of getting a sample mean of 24.8 years or older simply from natural sampling variation is equal to theP-value.

e) What's yourconclusion? Use a significance level of =.05. Choose the correct answer below.

A.

There is not enough evidence to suggest that the mean age of online shoppers has decreased from the mean of 24.8 years.

B.

There is enough evidence to suggest that the mean age of online shoppers has increased from the mean of 24.8 years.

C.

There is enough evidence to suggest that the mean age of online shoppers has decreased from the mean of 24.8 years.

D.

There isnot enough evidence to suggest that the mean age of online shoppers has increased from the mean of 24.8 years.