Question

A.) Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of ? = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 33 waves showed an average wave height of

x = 16.5 feet. Previous studies of severe storms indicate that ? = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use ? = 0.01.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to two decimal places.)

B.) A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.82 years. However, it is thought that the overall population mean age of coyotes is ? = 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 ? = 0.01.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

C.) Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7 2.9 3.8 4.2 4.8 3.1

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.70 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.45 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.45 grams? Use ? = 0.10.

What is the level of significance?

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

D.) 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 ? = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

E.) Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of

? = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.1 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.01.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

F.) 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).

91

89

82

104

99

108

82

91

The sample mean is x ? 93.3. 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 ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml. Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05.

What is the level of significance?

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

G.) Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.

14

19

16

19

15

11

15

16

17

12

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=
s	=

(ii) Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

H.) Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.

4.9

4.2

4.5

4.1

4.4

4.3

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=
s	=

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use ? = 0.05.

What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer 1

A) The level of significance = 0.01

The test statistic z = ()/()

                              = (16.5 - 16.4)/(3.5/)

                              = 0.16

B) The level of significance = 0.01

The test statistic t = ()/(s/)

                             = (2.05 - 1.75)/(0.82/)

                             = 2.481

C) The level of significance = 0.10

The test statistic z = ()/()

                              = (3.75 - 4.45)/(0.7/)

                             = -2.45

D) The level of significance = 0.05

The test statistic t = ()/(s/)

                             = (18.4 - 19)/(3.5/)

                             = -1.16

E) The level of significance = 0.01

The test statistic t = ()/(s/)

                            = (7.1 - 8)/(2.1/)

                            = -2.571

F) The level of significance = 0.05

The test statistic z = ()/()

                              = (93.3 - 85)/(12.5/)

                              = 1.88

P-value = P(Z > 1.88)

             = 1 - P(Z < 1.88)

             = 1 - 0.9699

             = 0.0301

G) i) = 15.4

       s = 2.63

ii) The level of significance = 0.01

The test statistic t = ()/(s/)

                             = (15.4 - 14)/(2.63/)

                             = 1.683

H) i) = 4.4

        s = 0.28

ii) The level of significance = 0.05

The test statistic t = ()/(s/)

                             = (4.4 - 4.64)/(0.28/)

                             = -2.100