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1. A severe storm has an average peak wave height of â€“ 16.4 feet for waves hitting the shore. Suppose that a Norâ€™easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land off fixed cement piers. Suppose that a reading of 36 waves showed an average wave height of xbar = 17.3 feet. Previous studies of severe storms indicate that = 3.5 feet. Does this information suggest that the storm is increasing above the severe rating? Use a = 0.01.

a) What is the level of significance? State the null and alternate hypothesis.

b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic?

c) Find or estimate 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 a?

e) State your conclusion.

2. Nationally, about 11% of the total US wheat crop is destroyed each year by hail. An insurance co. is studying wheat hail damage claims in Weld Co. A random sample of 16 claims in Weld Co gave the following data (% wheat crop lost to hail)

15, 8, 9, 11, 12, 20, 14, 11, 7, 10, 24, 20, 13, 9, 12, 5

The sample mean is xbar = 12.5%. Let x be a random variable that represents the percentage of wheat crop in Weld Co. lost to hail. Assume that x has a normal distribution and = 5.0%. Do these data indicate that the percentage of wheat crops lost to hail in Weld Co. 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 hypothesis.

b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic?

c) Find or estimate 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 a?

e) State your conclusion.

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