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 μ = 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 of 39 waves showed an average wave height of x = 17.2 feet. Previous studies of severe storms indicate that σ = 3.8 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.) test statistic = critical value = State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Reject the null hypothesis, there is insufficient evidence that the average storm level is increasing. Fail to reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Fail to reject the null hypothesis, there is insufficient evidence that the average storm level is increasing. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? The conclusions obtained by using both methods are the same. We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

Consider the following time series data:

Month 1 2 3 4 5 6 7

Value 25 14 19 11 18 22 16

(a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation.

(b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place.

Going back to problem 1, in real life you can, without much difficulty, get the mean grades of Prof. Lax’s classes but that is about it; meaning you will have no idea how his grades would be distributed, nor would you have any idea about the standard deviation of these grades. (I doubt Prof. Lax would advertise his laxness on his website. Contrary what you might believe that is academically bad form and might negatively affect his students’ hireability in the job market). However, you have access to Miss Z’s data (which she swears is obtained by a random selection process) and the grades she obtained in her random sample of nine were:

79, 75, 84, 63, 98, 52, 87, 99, 83

a .to help Miss Z with her decision to take this course with Prof. Lax or not, create a 97% confidence interval (CI) for the mean using Miss Z.’s data. Make sure that you do the necessary checks.

b. Does your interval capture the rumored population mean of 85?

c. Calculate the margin of error (ME or simply E) of your confidence interval.

d. Miss Z thinks a margin of error (or E) of 7 points or more will have a significant negative effect on her GPA. How does the ME (or E) of your 97% CI from part (c) compare to what she says her GPA can afford? If your CI’s ME (or E) is different than 7 points she can afford what are the ways you can use to reduce the margin of error down to 7 or smaller. Discuss all that can be done. 3

When evaluating research, what factors should be considered? Why are these factors important? Provide some examples to illustrate the importance of each factor.

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean mu equals280 days and standard deviation sigma equals12 days. ​(a) What proportion of pregnancies lasts more than 295 ​days? ​(b) What proportion of pregnancies lasts between 259 and 283 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 262 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 250 days. Are very preterm babies​ unusual?

For each of the following cases, assume a sample of n observations is taken from a normally distributed population with unknown mean μ and unknown variance σ2. Complete the following: i) Give the form of the test statistic. ii) State and sketch the shape of the prob. distribution of the test statistic when the null hypothesis is true. iii) Give the range of values of the test statistic which comprises the rejection region. iv) Sketch in the area(s) associated with α on the probability distribution of the test statistic. v) Compute the observed value of the test statistic. Give the approximate size of the p-value. vi) Using the observed value of the test statistic, state your conclusions with the appropriate probability statement. a. H0: σ2< 15; HA: σ2> 15, α = .05, n = 50, s2= 19.5

b. H0: σ2= 20 ; HA: σ2≠20, α = .05, n = 50, s2= 22.1

Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions.

(a) What percent of students scored above an 88 ?Round your answer to one decimal place.

(b) What percent of students scored below a 59 ?Round your answer to one decimal place.

(c) If the lowest 7%of students will be required to attend peer tutoring sessions, what grade is the cutoff for being required to attend these sessions?Round your answer to one decimal place.

(d) If the highest 9%of students will be given a grade of A, what is the cutoff to get an A? Round your answer to one decimal place.

What is factor analysis? in which situation is it useful?

Retaking the SAT (Raw Data, Software Required): Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. The Senior year scores (x) and associated Junior year scores (y) are given in the table below. This came from a random sample of 35 students. Use this data to test the claim that retaking the SAT increases the score on average by more than 27 points. Test this claim at the 0.01 significance level. (a) The claim is that the mean difference (x - y) is greater than 27 (μd > 27). What type of test is this? This is a left-tailed test. This is a two-tailed test. This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t d = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (e) Choose the appropriate concluding statement. The data supports the claim that retaking the SAT increases the score on average by more than 27 points. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 27 points. We reject the claim that retaking the SAT increases the score on average by more than 27 points. We have proven that retaking the SAT increases the score on average by more than 27 points. Senior Score (x) Junior Score (y) (x - y) 1093 1063 30 1238 1195 43 1238 1186 52 1112 1099 13 1289 1248 41 1109 1098 11 1061 1055 6 1102 1056 46 1139 1087 52 1090 1076 14 1157 1118 39 1263 1223 40 1279 1240 39 1117 1086 31 1226 1191 35 1216 1187 29 1324 1268 56 1199 1173 26 1279 1244 35 1165 1128 37 1151 1124 27 1159 1124 35 1256 1224 32 1255 1231 24 1129 1093 36 1299 1270 29 1261 1207 54 1207 1187 20 1156 1147 9 1177 1150 27 1253 1234 19 1320 1274 46 1200 1122 78 1234 1213 21 1143 1143 0

Q 15 Question 15 Consider the following sample of 11 length-of-stay values (measured in days): 1, 1, 3, 3, 3, 4, 4, 4, 4, 5, 7 Now suppose that due to new technology you are able to reduce the length of stay at your hospital to a fraction 0.5 of the original values. Thus, your new sample is given by .5, .5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 3.5 Given that the standard error in the original sample was 0.5, in the new sample the standard error of the mean is _._. (Truncate after the first decimal.)

Question 2: The efficacies of two drugs, X and Y were evaluated in two groups of mice (Group C, Group D). The outcome was the concentration of the drug in the plasma after giving the mice drugs (through drinking water) for 24 hours. The data were summarized below.

Question 2A. At the significance level of 0.05, are the drug concentrations in Group C and Group D different? Using Mann-Whitney U test here.

3. A nursing professor was curious as to whether the students in a very large class she was teaching who turned in their tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the mean? Explain. 8 points a. Yes, the students scored significantly different because they are right of the mean. b. No, the students did not score significantly different because they are less than 2 standard deviation from the mean.

Run a multiple regression with trend and seasonal; forecast the next 12 months.   

Two pea plants are crossed. Both are heterozygous for purple blossom color, while one is homozygous for being short and the other is heterozygous for being tall. In pea plants, tall is dominant to short, and purple flowers are dominant to white.

Fill out the table below for the probability of each possible phenotype. Report probability as a decimal rounded to four places (e.g. 0.1250, not 1/8 or 12.5%).

In a population of 150 pea plants, there are 53 tall-purple plants, 52 short-purple plants, 22 tall-white plants, and 23 short-white plants. In order to test if the two traits are experiencing independent assortment researchers would perform a chi squared test. The (null/alternative)  hypothesis states that the two genes are independently assorted while the (null/alternative)  hypothesis states the two genes are dependent.

What is your calculated Chi Squared statistic?

• When performing a contingency table, do not round your expected values!!
• Report your calculated X² rounded to four decimal places

What is the corresponding P value?

• Use the formula =1-(CHISQ.DIST(X²,df,TRUE)) to convert calculated X^{2 _{into a P value}}
• Report your answer rounded to 4 decimal places

Do you fail to reject or reject the null hypothesis?

As a result of this statistical analysis, it is possible to conclude that pea plant height and pea plant blossom color (are or are not)  linked traits.