Question

The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, 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 = 4.1. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.10. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 18; H1: μ ≠ 18; two-tailed H0: μ = 18; H1: μ < 18; left-tailed H0: μ = 18; H1: μ > 18; right-tailed H0: μ ≠ 18; H1: μ = 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with unknown σ. The Student's t, since we assume that x has a normal distribution with known σ. The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ. 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.) Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.10 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18 There is insufficient evidence at the 0.10 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

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 claimsin the county reported the percentage of their wheat lost to hail.

17	7	10	11	14	20	13	9
9	10	23	21	13	11	12	5

The sample mean is x = 12.8%. 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.

(a) What is the level of significance?




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.)

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.

32

23

43

35

28

37

31

The sample mean is x ≈ 32.7 ml/kg. 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?

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.)

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 82 students shows that 39 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

What are we testing in this problem?

single proportionsingle mean     

(a) What is the level of significance?

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

The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.32 A, with a sample standard deviation of s = 0.43 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

(a) What is the level of significance?

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

A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 44 of 93 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped.

What are we testing in this problem?

single proportionsingle mean     

(a) What is the level of significance?


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

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 8. A random sample of 90 matchboxes shows the average number of matches per box to be 43.0. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?

What are we testing in this problem?

single proportionsingle mean     

(a) What is the level of significance?

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

The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 121 employees in the private sector showed that 32 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05.

What are we testing in this problem?

single proportionsingle mean     

(a) What is the level of significance?


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

A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of ten cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.60 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance.

What are we testing in this problem?

single proportionsingle mean     

(a) What is the level of significance?


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

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months):

29

44

43

48

53

46

30

51

42

52

(i) Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s. (Round your answers to two decimal places.)

x =	months
s =	months

(a) What is the level of significance?

Answer 1

Sal Null othesisHo: =18. The dala indicate that the plE 1atio l all us.bank stoces is 18 Altenative hy pothesis! H HC18. The dala indiate that tha p/E aio all u.s. bank stoCE Is dass than he use 2-test, g the shndad nona Strre we nosmal aistbuton otth assume tŁ host X has a Cnocon 2-statistic New 2- 17-1-18 -O8213 The P-vaieis O-205823 The result is not sig AGt at Po10 tHen Condusioncine p-value js gieakr than o10 Hen te we Gndudo we the dala Kndiae that the PIE atio p that all b.s.banic stociks is 18