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 7 7 9 11 19 12 12 98 24 20 12 8 13 5 The sample mean is x = 11.8%. 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 a = 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? O Ho: H=11%; H₁: # Ho: 11%; H₁ Ho: 11%; H₁: Ho: H = 11%; H₁: 11%; two-tailed = 11%; two-tailed > 11%; right-tailed < 11%; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ. The Student's t, 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 known σ. The standard normal, since we assume that x has a normal distribution 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. -2 -1 0 1 2 -2 2 (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 a? At the a=0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a=0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a=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.

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The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.
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 7 7 9
11 19 12 12
98 24 20 12 8 13 5
The sample mean is x = 11.8%. 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 a = 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?
O Ho: H=11%; H₁:
#
Ho: 11%; H₁
Ho: 11%; H₁:
Ho: H = 11%; H₁:
11%; two-tailed
= 11%; two-tailed
> 11%; right-tailed
< 11%; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling
distribution.
The Student's t, since n is large with unknown σ.
The Student's t, 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 known σ.
The standard normal, since we assume that x has a normal distribution 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.
-2
-1
0
1
2
-2
2
(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 a?
At the a=0.01 level, we reject the null hypothesis and conclude the data are statistically
significant.
At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically
significant.
At the a=0.01 level, we fail to reject the null hypothesis and conclude the data are statistically
significant.
At the a=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.
Transcribed Image Text: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 7 7 9 11 19 12 12 98 24 20 12 8 13 5 The sample mean is x = 11.8%. 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 a = 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? O Ho: H=11%; H₁: # Ho: 11%; H₁ Ho: 11%; H₁: Ho: H = 11%; H₁: 11%; two-tailed = 11%; two-tailed > 11%; right-tailed < 11%; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ. The Student's t, 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 known σ. The standard normal, since we assume that x has a normal distribution 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. -2 -1 0 1 2 -2 2 (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 a? At the a=0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a=0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a=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.
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