Question

A marketing researcher wants to estimate the mean amount spent per year​ ($) on a web site by membership member shoppers. Suppose a random sample of 100 membership member shoppers who recently made a purchase on the web site yielded a mean amount spent of $55 and a standard deviation of $54.

a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from $47? (Use .10 level of significance.) State the null and alternative hypotheses.

b. Identify the critical values.

c. Determine the test statistic.

d. Do Not Reject/Reject H0. there is Insufficient/Sufficient evidence that the population mean spent by membership member customer is different from $47.

e. Determine the p-value and interpret its meaning.

Answer 1

Solution :

= 47

= 55

S = 54

n = 100

a ) This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 47

Ha :     47

b ) The significance level is α =0.10, and the critical value for a two-tailed test is tc = 1.66

c ) Test statistic = t

= ( - ) / S / n

= (55 - 47) / 54 / 100

= 1.481

Test statistic = t =  1.481

P-value =0.1417

= 0.10

P-value <

0.1417 ≥ 0.10

d )Fail to reject the null hypothesis .

e )There is insufficient evidence that the population mean spent by membership member customer is different from $47.