Testing the Mean Worksheet
1. For a student’s 𝑡 distribution with 𝑑. 𝑓. = 10 and 𝑡 = 2.93
a) Find an interval containing the corresponding 𝑃 − 𝑣𝑎𝑙𝑢𝑒 for a two – tailed test
b) Find and interval containing the corresponding 𝑃 − 𝑣𝑎𝑙𝑢𝑒 for a right – tail test
2. A random sample had 49 values. The sample mean is 8.5 and the sample standard
deviation is 1.5. Use a level of significance of 0.01 to conduct a left – tailed test of the
claim that the population mean is 9.2
a) Find the null and alternate hypotheses
b) Compute the sample test statistic 𝑡
c) Estimate the 𝑃 − 𝑣𝑎𝑙𝑢𝑒 for the test
d) Do we reject or fail to reject 𝐻0
3. Let 𝑥 be a random variable that represents the pH of arterial plasma. For healthy
adults, the mean of the 𝑥 distribution is 𝜇 = 7.4. A new drug for arthritis has been
developed. However, it is thought that this drug may change blood pH. A random
sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed
that 𝑥̅ = 8.1 with sample standard deviation 𝑠 = 1.9 . Use a 5% level of significance
to test the claim that the drug has changed ( either way ) the mean pH level of blood.
4. A random sample of 46 adult coyotes in a region of northern Minnesota showed the
average age to be 𝑥̅ = 2.05 years, with sample standard deviation 𝑠 = 0.82 years. It
is thought that the overall population mean age of coyotes is 𝜇 = 1.75 years. Do the
sample data indicate that coyotes in this region of northern Minnesota tend to live
longer than the average of 1.75 years ? Use 𝛼 = 0.01
5. 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 data : 𝑥̅ = 71.4 years , 𝑠 = 20.65 years.
Assuming that life span in Honolulu is approximately normally distributed, does this
information indicate that the population mean life span for Honolulu residents is
less than 77 years ? Use a level of significance of 5%.
6. The ski patrol at Vail, Colorado is studying a common type of avalanche called a slab
avalanche. Slab avalanches in Canada have an average thickness of 𝜇 = 67 cm. A
random sample of avalanches in spring gave the following thicknesses ( in cm ) :
59
68
51
55
76
64
38
67
65
63
54
74
49
65
62
79
a) Find 𝑥̅ and 𝑠 using a calculator.
𝑥̅ = __________
𝑠 = __________
b) Assume the slab thickness has an approximately normal distribution. Use a 1%
level of significance to test the claim that the mean slab thickness in the Vail
region is different from that in Canada.