1.

Give as much information as you can about the P-value of a t test in each of the following situations. (Round your answers to three decimal places.)

(a)

upper-tailed test, df = 7,

t = 2.0

(b)

upper-tailed test, n = 14,

t = 3.5

(c)

lower-tailed test, df = 10,

t = 2.7

(d)

lower-tailed test, n = 23,

t = 4.3

You may need to use the appropriate table in the appendix to answer this question.

2. A certain pen has been designed so that true mean writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 17 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H₀: = 10

versus H_a: < 10.

(a)

If t = 2.2

and = 0.05

is selected, what conclusion is appropriate?

Reject Fail to reject

(b)

If t = 1.73

and = 0.01

is selected, what conclusion is appropriate?

Reject Fail to reject

(c)

If t = 0.57,

what conclusion is appropriate?

Reject Fail to reject

You may need to use the appropriate table in the appendix to answer this question.

3. A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,945. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,600 and a standard deviation of $3,900. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945? Test the relevant hypotheses using = 0.05.

Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value=

State your conclusion.

Reject H₀. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945. Reject H₀. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945. Fail to reject H₀. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945. Fail to reject H₀. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945.

You may need to use the appropriate table in the appendix to answer this question.

4. 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). 5.19 4.98 4.04 4.69 5.25 4.64 4.16 4.99 5.18 5.58 5.32 4.60

The mean price of this hamburger in the U.S. in January was $4.61. 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 = 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=

State your conclusion.

Do not reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Do not reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

You may need to use the appropriate table in the appendix to answer this question.

5. 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 $9.14 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=

State your conclusion.

Reject H₀. We do not have convincing evidence that the mean minimum purchase amount for which Canadians consider it acceptable to use a debit card is less than $10. Reject H₀. We have convincing evidence that the mean minimum purchase amount for which Canadians consider it acceptable to use a debit card is less than $10. Do not reject H₀. We do not have convincing evidence that the mean minimum purchase amount for which Canadians consider it acceptable to use a debit card is less than $10. Do not reject H₀. We have convincing evidence that the mean minimum purchase amount for which Canadians consider it acceptable to use a debit card is less than $10.