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 of33waves 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 ftH₀:= 16.4 ft;H₁:> 16.4 ft H₀:= 16.4 ft;H₁:16.4 ftH₀:> 16.4 ft;H₁:= 16.4 ftH₀:< 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 unknown.The standard normal, since the sample size is large andis known. 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 > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-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.

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean isx= 3.75 grams. Letxbe a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatxhas a normal distribution and=0.94gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.70grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.70grams?Use=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:= 4.7 g;H₁:> 4.7 g; right-tailedH₀:= 4.7 g;H₁:4.7 g; two-tailed H₀:= 4.7 g;H₁:< 4.7 g; left-tailedH₀:< 4.7 g;H₁:= 4.7 g; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student'st, sincenis large with unknown.The Student'st, since we assume thatxhas a normal distribution with known. The standard normal, since we assume thatxhas a normal distribution with known.The standard normal, since we assume thatxhas a normal distribution with unknown.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) 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) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.70 grams. There is insufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.70 grams.

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of9.7minutes and a standard deviation of2.3minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)(a) less than 10 minutes (b) longer than 5 minutes