Probability and Statistics
HW 7 – Z and T Test Practice
Name_______________________________
1.
Test the claim that only children have an average higher cholesterol level than the national average. It
is known that the mean cholesterol level for all Americans is 190 and the standard deviation is 15. In a
sample of 100 children, the average cholesterol content was198. Use a significance level of 0.01.
2.
Suppose that we want to test the hypothesis with a significance level of 0.05 that the climate has
changed since industrialization. Suppose that the mean temperature throughout history is 50 degrees.
During the last 40 years, the mean temperature has been 51 degrees and the population standard
deviation is 2 degrees. What can we conclude?
3.
Suppose Gap, the clothing store, wants to introduce their line of clothing for women to another country.
Their clothing sizes are based on the assumption that the average size of a woman is 162 cm. To
determine whether they can simply ship the clothes to the new country they select 5 women at random
in the target country and determine their heights as follows:
149, 165, 150, 158, 153
Should they adjust their line of clothing or ship them without change? Use a significance level of 0.05.
4.
When 14 different 2nd year medical students measured the systolic blood pressure of the same person,
they found the average blood pressure was 137 mmHg and the standard deviation to be 10 mmHg.
Using a 0.05 significance level, test the claim that the mean blood pressure level is less than 140 mm
Hg. Hypertension is defined to be a blood pressure level that is too high because it is 140 mm Hg or
greater. Based on the hypothesis test results, can it be safely concluded that the person does NOT have
hypertension?
5.
50 smokers were questioned about the number of hours they sleep each day. We want to test the
hypothesis that the smokers need less sleep than the general public which needs an average of 7.7 hours
of sleep with a standard deviation of 0.5. The average amount of sleep needed from the sample group
was 7.5 hours. Use a significance level of 0.05.
6.
Test the hypothesis that the mean age of a population is at most 30, given a random sample of 10
individuals who have a mean of 27 and a sample variance of 20. Use a significance level of 0.10.
7.
Test the hypothesis that the body mass index of a sample of 14 males is not 35. The sample mean is
30.5 and the sample standard deviation is 10.6392. Use a significance level of 0.01.
8.
Randomly selected statistics students participated in an experiment to test their ability to determine
when 60 seconds has passed. 40 students yielded a sample mean of 57.3 seconds. Assuming that
  9.5 seconds, use a 0.05 significance level to test the claim that the population mean is equal to 60
seconds.
9.
A simple random sample of 40 salaries of professional football coaches has a mean of $417,421. The
standard deviation of all salaries of professional football coaches is $466,181. Use a 0.01 significance
level to test the claim that the mean salary of a professional football coach is less than $500,000.
10. USA Today reported that the state with the longest mean life span is Hawaii, where the population
mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave
the following information about life span (in years) of Honolulu residents:
72
77
68
69
81
85
93
97
56
75
19
71
78
86
94
47
83
66
84
27
Assuming that life span in Honolulu is approximately normally distributed, does this information
indicate that the population mean life span for Honolulu residents is more than 77 years? Use a 5%
level of significance.
NOTE: Use find the sample mean to the nearest tenth and the st. deviation to the nearest hundredth.