Weatherwise is 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 u- 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm dass rating. Peak wave heightsare usually measured from land (using binoculars) off foxed cement piers. Suppose that a reading of 36 waves showed an average wave height of x- 16.9 feet. Previous studies of severe storms indicate that - 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use a - 0.01.(a) What is the level of significance?OState the null and alternate hypotheses.O H: - 16.4 ft; H,: > 16.4 ftO Ho H< 16.4 t; H: - 16.4 ftO Hoi H- 16.4 ft; H:< 16.4 ftO H- 16.4 t; H: + 16.4 tOHi > 16.4 t; H,: - 16.4 m(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.O The standard normal, since the sample size is large and o is known.O The Student's t, since the sample size is large and o is known.O The standard normal, since the sample size is large and o is unknown.O The Student's t, since the sample size is large and o is unknown.What is the value of the sample test statistic? (Round your answer to two decimal places.)(c) Estimate the P-value.O Pvalue > 0.250O 0.100 < P-value < 0.250O 0.050 < Pvalue < 0.100O 0.010 < Pvalue < 0.050O Pvalue 0.010Sketch the sampling distribution and show the area corresponding to the Pvalue.o-3-2-1123o-3-2-1 012O-3-2-112o-3-2-1123(d) Based on your answers in parts (a) to (C), wil you reject or fail to reject the nul hypothesis? Are the data statistically significant at level a?O At the a- 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.O At the a- 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the a- 0.01 level, we fail to reject the null hypothesis and condude the data are statistically significant.O At the a- 0.01 level, we fail to reject the null hypothesis and condude the data are not statistically significant.(e) Interpret your condusion in the context of the application.O There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.O There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

a) Assume that μ is the population mean height of wave.

Wearherwise is a magaaine published by the American Meteorological Society. One isue gives a rating system used to dassity Noreaster storms that frequently hit New England and can cause much damage near the ocean, A severe starm has an average peak wave height of -16.4 feet for waves Ntting the shere. Suppase that a Noreaster is in progress at the severe storm dass rating. Peak wave heights are utually measured from land (using binoculars) oft fed cement piers. Suppose that a reading of 36 waves showed an average wave height of 16.9 feet. Previous studies of severe storms indicate that-3.5 feet. Does this information suggest that the storm is (perhaps temporaniy) increasing above the severe rating? Use a0.01. Ca) what is the level of significancet State the nul and aternate hypatheses. O Hi16.4 n, H 164n OMgi 164 n, 164n OMi 164 n, 164 (b) What sampling distribution wil you use Explain the rationale for your choice of samaling distribution. O The standard normal, since the sample size is large ande is known. O The Student's t, since the samale sie is large and eis known. O The standard normal, since the sample size is large ande is unknown. O The Student's t, since the sample siae is large and e is unknown What is the value of the sample test statiusc (Round your answer to two decimal places.) (4) Estimane the Avalue. OPvalue 0.250 O0.100 Avalue0.250 O0.0s0 Pvalue.100 O0.010 Pvalue0.0s0 OPvalue 0.010 Skatch the samgling dstribution and show the area comesponding to the Pvalue. 0-3 (4) Based on your aniwers in parts (a) to (), will you reject or fall to reject the nul hypothesis Are the data statistically significant a levela O the e0.01 evel, we reject the null hypothesis and condude the data are statistically signiicart. OA the e0.01 evel, we reject the null hypsthesis and condude the data are not statistically signiticant. OM the e0.01 level, we fail to reject the null hypothesis and condude the data are statistically signincant. OA the e001 evel, we fail to reject the null hypothesis and condude the data are not statistically signiicant. . (4) Interpret your condusion in the context of the application. O There is suficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. O There s insumdent evidence at the 0.01 evel to conclude that the starm is increaing above the severe rating.