1, Test the claim about the difference between two population means 1 and 2 at the level of significance . Assume the samples are random andindependent, and the populations are normally distributed.

Claim:

12,

=0.10.

Assume

2122

Samplestatistics:

x1=2416,

s1=171,

n1=15

and

x2=2303,

s2=55,

n2=9

.

Find the standardized test statistic t.

t=

(Round to two decimal places asneeded.)

Find theP-value.

P=

(Round to three decimal places asneeded.)

2, Preliminary data analyses indicate that you can consider the assumptions for using non-pooledt-procedures satisfied. Researchers randomly and independently selected 33 prisoners diagnosed with chronic posttraumatic stress disorder(PTSD) and 21prisoners that were diagnosed with PTSD but had since recovered(remitted). Theages, inyears, at arrest yielded the summary statistics shown in the table to the right. At the

10% significancelevel, do the data provide sufficient evidence to conclude that a difference exists in the mean age at arrest of prisoners with chronic PTSD and remittedPTSD?

Chronic remitted

x1 = 25.5 x2 = 21.3

s1 = 2 s2 = 7

n1 = 34 n2 = 21

Find the test statistic.

t=

(Round to three decimal places asneeded.)

Find theP-value.

P=

(Round to four decimal places asneeded.)

3, Preliminary data analyses indicate that you can consider the assumptions for using non-pooledt-procedures satisfied. Researchers obtained the data shown in the table on the number of acute postoperative days in the hospital using dynamic and static systems. At the 5% significancelevel, do the data provide sufficient evidence to conclude that the mean number of acute postoperative days in the hospital is smaller with the dynamic system than with the staticsystem?

(Note:

x1=6.92,

s1=1.73,

x2=10.50,

and

s2=4.93)

Find the test statistic.

t=

(Round to three decimal places asneeded.)

Find theP-value.

P=

(Round to four decimal places asneeded.)

4, A researcher randomly selects 6 fathers who have adult sons and records thefathers' andsons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the =0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a pairedt-test is reasonable.

Observation

1

2

3

4

5

6

Height of father(in inches)

72.3

74.5

72.1

68.2

73.4

65.4

Height of son(in inches)

74.1

78.6

74.3

72.9

76.0

68.8

74.1

78.6

74.3

72.9

76.0

68.8

Find the test statistic.

t=

(Round to three decimal places asneeded.)

Find theP-value.

P-value=

(Round to four decimal places asneeded.)

5, A survey of 500 workers showed that 161said it was unethical to monitor employeee-mail. When

125 senior-level bosses weresurveyed, 42 said it was unethical to monitor employeee-mail. At the 1%

significancelevel, do the data provide sufficient evidence to conclude that the proportion of workers that

Calculate the test statistic. say monitoring employeee-mail is unethical is less than the proportion ofbosses?

z=

(Round to two decimal places asneeded.)

Calculate theP-value.

P=

(Round to three decimal places asneeded.)

6, An insurance company collects data onseatbelt use among drivers in a country. Of 1900 drivers 20-29 yearsold, 27% said that they buckleup, whereas 455 of 1600 drivers 45-64 years old said that they did. At the 1% significancelevel, do the data suggest that there is a difference inseatbelt use between rivers

20-29 years old and those 45-64? Let population 1 be drivers of age 20-29 and let population 2 be drivers of age 45-64. Use thetwo-proportions z-test to conduct the required hypothesis test. What are the hypotheses for thistest?

Calculate the test statistic.

z=

(Round to two decimal places asneeded.)

Calculate theP-value.

P=

(Round to three decimal places asneeded.)