Question

A) A polling organization reported data from a survey of 2000 randomly selected Canadians who carry debit cards. Participants in this survey were asked what they considered the minimum purchase amount for which it would be acceptable to use a debit card. Suppose that the sample mean and standard deviation were $9.17 and $7.50, respectively. (These values are consistent with a histogram of the sample data that appears in the report.)

Do these data provide convincing evidence that the mean minimum purchase amount for which Canadians consider the use of a debit card to be appropriate is less than $10? Carry out a hypothesis test with a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

B) A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

5.16	4.99	4.07	4.66	5.28	4.67
4.12	4.96	5.19	5.59	5.33	4.60

The mean price of this hamburger in the U.S. in January was $4.62. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

Answer 1

Q A)

Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

The P-Value is =0.000

Since p value is less than significance level, Reject H0.

Hence, at 1% significance level, we have enough evidence to support the claim that the mean minimum purchase amount for which Canadians consider the use of a debit card to be appropriate is less than $10.

Q B)

Null Hypothesis

Alternative Hypothesis

The sample mean is

The sample Standard deviation is

Under H0, the test statistic is

Degrees of freedom = n-1= 12-1=11

The P-Value is 0.039

Since p value is less than significance level. Reject H0.

Hence, at 5% significance level, we have sufficient evidence to support the claim that the mean January price of this hamburger in Europe is greater than $4.62