The average age of online consumers a few years ago was 24.3 years As older indi

Question

The average age of online consumers a few years ago was 24.3 years As older individuals gain confidence with the internet it is believed that the average age has increased. We would like to test this belief. Answer parts a) through e) below. a) Write the appropriate hypotheses. Choose the correct answer below. A. H_0:mu 24.3 year C. H_0:mu = 24.3 years H_A:mu 24 3 years H_A:mu = 24.3 years b) We plan to test the null hypothesis by selecting a random sample of 36 individuals who have made an online purchase this year. Do you think the necessary assumptions for inference are satisfied? Explain. Choose the correct answer below. A. No The sample was not selected random, which violates the independence Assumption. B. No the sample is not large enough to safety assume that the Nearly Normal Condition is satisfied. C. Yes The Independence Assumption is met since the sample was selected randomly The Nearly Normal Condition is met since the sample of 36 shoppers is likely large enough to be safe to proceed (given that there is not any outliers or serious skewness in the distribution) D. Yes. More than 10% of the sample was selected randomly, which satisfies the Independence Assumption. Furthermore a sample of 36 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 c) The online shoppers in our sample had an average age of 25.5 years with a standard deviation of 5.2 years. Whats the P value for this result? The P-value is. (Round to three decimal places as needed.) d) Explain (in context) what this P-value means Choose the correct answer below A. The probability of a random sample of 36 shoppers having an age less than the hypothesized mean age is equal to the P-value B. If the mean age of shoppers remains at 24.3 years, the probability of getting a sample mean of 25.5 years or older simply from natural sampling variation is equal to the P-value. C. If the mean age of shoppers remains at 25.6 years, the probability of getting a sample mean of 24.3 years or older simply from natural sampling variation is equal to the P-value. D. The probability of a random sample of 36 shoppers having an age more than the hypothesized mean age is equal to the P-value. e) What's your conclusion? Use a significance level of alpha = .05 Choose the correct answer below. A. There is enough evidence to suggest that the mean age of online shoppers has increased from the mean of 24.3 years B. There Is not enough evidence to suggest that the mean age of online shoppers has decreased from the mean of 24.3 years. C. there is enough evidence to suggest that the mean age of online shoppers has decreased from the mean of 24.3 years.

Explanation / Answer

a) option B is correct

b)option C is correct

c)here std error =std deviation/(n)1/2=0.8667

hence test stat t=(X-mean)/std error =(25.5-24.3)/0.8667=1.3846

for above at 35 degree of freedom p value =0.087

d)option B is correct

e)option A is correct

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