Question

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 3.1%. A random sample of 10 bank stocks gave the following yields (in percents).

5.7

4.8

6.0

4.9

4.0

3.4

6.5

7.1

5.3

6.1

The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? Use α = 0.01.

(c) Find (or estimate) the P-value.

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

80

103

100

109

85

89

The sample mean is x ≈ 93.9. 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.

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

(c) Find (or estimate) the P-value.

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 σ = 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use α = 0.10.

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


(c) Find (or estimate) the P-value.

The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (JP Morgan Chase, Bank of America, and others) gave the following P/E ratios.†

24	16	22	14	12	13	17
22	15	19	23	13	11	18

The sample mean is

x ≈ 17.1.

Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is μ = 18. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and σ = 4.9. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.01.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value.

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.

17	10	9	9	11	22	13	11
7	8	25	18	11	10	12	6

The sample mean is x = 12.4%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01.

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

(c) Find (or estimate) the P-value

Answer 1