Question

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...

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 7 9 13 13 20 13 11 5 8 26 21 13 8 12 4

The sample mean is x = 12.5%. 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?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H0: μ ≠ 11%; H1: μ = 11%; two-tailed

H0: μ = 11%; H1: μ > 11%; right-tailed

H0: μ = 11%; H1: μ ≠ 11%; two-tailed

H0: μ = 11%; H1: μ < 11%; left-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 known σ.

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.

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.

(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 = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 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 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.

There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.

Homework Answers

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.01

H0: μ = 11%; H1: μ ≠ 11%; two-tailed

b) The standard normal, since we assume that x has a normal distribution with known σ.

Sample test statistic = 1.20

c) P-value = 0.2301

d) At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e) There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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. 14 8 10 11 10 18 16 12 7 9 26 21 11 9 11 6 The sample mean is x = 12.4%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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. 13 8 9 9 14 18 16 9 5 10 22 21 11 11 12 3 The sample mean is x = 11.9%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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. 13 8 10 10 12 19 16 9 9 9 24 22 11 8 11 5 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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 7 7 11 11 20 13 10 8 11 25 18 12 10 11 4 The sample mean is x = 12.2%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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. 16 7 8 11 11 21 15 9 9 9 26 22 12 10 13 5 The sample mean is x = 12.8%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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 9 10 9 10 20 15 10 8 12 22 19 15 10 12 3 The sample mean is x = 12.6%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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. 13 6 10 13 12 20 16 9 7 8 25 18 15 9 14 6 The sample mean is x = 12.6%. Let x be a random variable that represents the percentage...
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An...
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 9 8 13 10 19 14 9 8 8 26 22 11 9 12 7 The sample mean is x = 12.6%. Let x be a random variable that represents the percentage...
Total blood volume (in ml) per body weight (in kg) is important in medical research. For...
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. 33 26 40 33 32 39 29 The sample mean is x ≈ 33.1 ml/kg. Let x...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.5%. 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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT