Weatherwiseis a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of= 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of30waves showed an average wave height ofx=16.5feet. Previous studies of severe storms indicate that= 3.5feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use= 0.01.(a) What is the level of significance?

State the null and alternate hypotheses.

H₀:< 16.4 ft;H₁:= 16.4 ft

H₀:> 16.4 ft;H₁:= 16.4 ft

H₀:= 16.4 ft;H₁:16.4 ft

H₀:= 16.4 ft;H₁:> 16.4 ft

H₀:= 16.4 ft;H₁:< 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large andis known.

The standard normal, since the sample size is large andis unknown.

The Student'st, since the sample size is large andis known.

The Student'st, since the sample size is large andis unknown.

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

(c) Estimate theP-value.

P-value > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-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?

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

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

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

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

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is= 19inches. However, a survey reported that of a random sample of51fish caught, the mean length wasx=18.6inches, with estimated standard deviations=3.4inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than= 19inches? Use= 0.05.(a) What is the level of significance?

State the null and alternate hypotheses.

H₀:< 19 in;H₁:= 19 in

H₀:= 19 in;H₁:19 in

H₀:= 19 in;H₁:< 19 in

H₀:> 19 in;H₁:= 19 in

H₀:= 19 in;H₁:> 19 in

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student'st, since the sample size is large andis known.

The standard normal, since the sample size is large andis known.

The Student'st, since the sample size is large andis unknown.

The standard normal, since the sample size is large andis unknown.

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

(c) Estimate theP-value.

P-value > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-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?

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.