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 ​$58 and a standard deviation of ​$55. Complete parts​ (a) and​ (b) below. a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from ​$51​? ​(Use a 0.01 level of​ significance.)   State the null and alternative hypotheses.

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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 ​$58
and a standard deviation of ​$55.
Complete parts​ (a) and​ (b) below.
a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from
​$51​?
​(Use a
0.01
level of​ significance.)
 
State the null and alternative hypotheses.
Expert Solution
Hypothesis Set up and Test Statistic

Assuming the samples are drawn from a normal population.

Null Hypothesis(H0):μ= $51Alternate Hypothesis(H1): μ$51

Given here is, Mean(μ)=58, Standard deviation(s)=55, and Size of sample(n)=100

The test statistic t is,t=x¯-μS2n  = x¯-μsn  ~t(n-1)   where sn is the standard ard error.

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