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 ​$60 and a standard deviation of ​$53. 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 ​$53​? ​(Use a 0.01 level of​ significance.)   State the null and alternative hypotheses.   H0​: μ equals=   5353 H1​: μ not equals≠   5353 ​(Type integers or decimals. Do not round. Do not include the​ $ symbol in your​ answer.) Identify the critical​ value(s).   The critical​ value(s) is/are 2.63 comma negative 2.632.63,−2.63. ​(Type an integer or a decimal. Round to two decimal places as needed. Use a comma to separate answers as​ needed.) Determine the test statistic.   The test​ statistic, tSTAT​, is 1.321.32. ​(Type an integer or a decimal. Round to two decimal places as​ needed.) State the conclusion.   Do not reject   H0. There is insufficient   evidence that the population mean spent by membership member customers is different from ​$53. b. Determine the​ p-value and interpret its meaning.   The​ p-value is . 190.190. ​(Type an integer or a decimal. Round to three decimal places as​ needed.) Interpret the meaning of the​ p-value. Select the correct answer below.     A. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than ​$7 above ​$53 if the null hypothesis is false.   B. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than ​$7 below ​$53 if the null hypothesis is false.   C. The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than ​$7 away from ​$53 if the null hypothesis is true.   D. The​ p-value is the probability of not rejecting the null hypothesis when it is false.

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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
​$60
and a standard deviation of
​$53.
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
​$53​?
​(Use a
0.01
level of​ significance.)
 
State the null and alternative hypotheses.
 
H0​:
μ
equals=
 
5353
H1​:
μ
not equals≠
 
5353
​(Type integers or decimals. Do not round. Do not include the​ $ symbol in your​ answer.)
Identify the critical​ value(s).
 
The critical​ value(s) is/are
2.63 comma negative 2.632.63,−2.63.
​(Type an integer or a decimal. Round to two decimal places as needed. Use a comma to separate answers as​ needed.)
Determine the test statistic.
 
The test​ statistic,
tSTAT​,
is
1.321.32.
​(Type an integer or a decimal. Round to two decimal places as​ needed.)
State the conclusion.
 
Do not reject
 
H0.
There is
insufficient
 
evidence that the population mean spent by membership member customers is different from
​$53.
b. Determine the​ p-value and interpret its meaning.
 
The​ p-value is
. 190.190.
​(Type an integer or a decimal. Round to three decimal places as​ needed.)
Interpret the meaning of the​ p-value. Select the correct answer below.
 
 
A.
The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than
​$7
above
​$53
if the null hypothesis is false.
 
B.
The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than
​$7
below
​$53
if the null hypothesis is false.
 
C.
The​ p-value is the probability of obtaining a sample mean that is equal to or more extreme than
​$7
away from
​$53
if the null hypothesis is true.
 
D.
The​ p-value is the probability of not rejecting the null hypothesis when it is false.
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