Statistics Worksheet

Ch. 9 Questions.2.) Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the
blood). 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 x = 8.8 with sample standard deviation s = 3.1. Use a 5% level of significance to test
the claim that the drug has changed (either way) the mean pH level of the blood.
A.) What is the level of significance?
B.) What is the value of the sample test statistic? (Round your answer to three decimal
places.)
4.) Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for
cutthroat trout. Suppose a friend tells you that the average length of trout caught in
Pyramid Lake is 𝜇 = 19 inches. However, a survey reported that of a random sample of
51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation
s = 3.1 inches. Do these data indicate that the average length of a trout caught in
Pyramid Lake is less than 𝜇 = 19 inches? Use 𝛼 = 0.05.
A.) What is the level of significance?
B.) What is the value of the sample test statistic? (Round your answer to three decimal
places.)
7.) A random sample of 51 adult coyotes in a region of northern Minnesota showed the
average age to be x = 2.03 years, with sample standard deviation s = 0.82 years.
However, it is thought that the overall population mean age of coyotes is 𝜇 = 1.75. 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.
A.) What is the level of significance?
B.) What is the value of the sample test statistic? (Round your answer to three decimal
places.)
8.) Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a
veterinarian took the following glucose readings from this horse (in mg/100 ml).
95
90
82
103
97
108
82
91
The sample mean is x ≈ 93.5. Let x be a random variable representing glucose readings
taken from Gentle Ben. We may assume that x has a normal distribution, and we know from
past experience that 𝜎 = 12.5. The mean glucose level for horses should be 𝜇 = 85 mg/100
ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher
than 85? Use 𝛼 = 0.05.
A.) What is the level of significance?
B.) Compute the z value of the sample test statistic. (Round your answer to two decimal
places.)
C.) Find (or estimate) the P-value. (Round your answer to four decimal places.)
11.) Total blood volume (in ml) per body weight (in kg) is important in medical research.
For healthy adults, the red blood cell volume mean is about 𝜇 = 28 ml/kg.† Red blood cell
volume that is too low or too high can indicate a medical problem. Suppose that Roger has
had seven blood tests, and the red blood cell volumes were as follows.
34
24
41
36
32
39
27
Let x be a random variable that represents Roger’s red blood cell volume. Assume that x
has a normal distribution and 𝜎 = 4.75. Do the data indicate that Roger’s red blood cell
volume is different (either way) from 𝜇 = 28 ml/kg? Use a 0.01 level of significance.
A.) What is the level of significance?
B.) Compute the z value of the sample test statistic. (Round your answer to two decimal
places.)
C.) Find (or estimate) the P-value. (Round your answer to four decimal places.)