6. Morning House is a mail-order firm which carries a wide range of rather expensive art objects for homes and offices. It operates by advertising a particular item either in selected magazines or in a direct-mail program. Suppose the sales response varies widely by item and the firm’s management has been unable to predict in advance which items will sell well and which will not. Consequently, the firm frequently experiences either stock-outs or excessive inventories. For many of the products Morning House sells, it is possible to order a limited amount for inventory and to place a subsequent order for delivery within two weeks. Thus, if the firm could make a early prediction of the ultimate sales of a product, its inventory problems would be greatly reduced. Since it takes approximately six weeks to receive 90% of the response to a given campaign, an accurate prediction of total sales made as late as the end of the first week of receiving orders would be useful. The first week’s sales and total sales of the last 12 campaigns of the firm are shown below. Can the first week’s sales be used to predict total sales? * Need help on minitab if this is a regression?

                        First week’s   Total

Campaign      Sales               Sales

1        32                    167

2                      20                    91

3                      114                  560

4                      66                    335

5                      18                    70

6                      125                  650

7                      83                    401

8                      65                    320

9                      94                    470

10                    5                      15

11                    39                    210

12                    50                    265

2. A city is hosting an annual marathon event and wants to produce t-shirts. Maria was able to obtain previous years’ demand and probability data as given in below table. She also estimates:

Selling price is $10, cost is $3, and the salvage value is $1.

Calculate all numbers in the payoff table. Show all work. How many shirts should be made to maximize profit?

The company you work for, Capital Capacitors, makes a specialized capacitor. Data from six different production months has been collected:

January: 58,000 produced February: 71,000 produced March: 72,000 produced

April: 50,000 produced May: 54,000 produced June: 63,000 produced

The cost to produce one of these capacitors has been estimated to be $1.20.

1. What are the upper and lower bounds of a 95% confidence interval on the mean number of capacitors produced per month?

2. At an interest rate of 1% per month, what is the projected yearly cost, low and high estimates? Use your lower and upper bounds from 1. in your computations.

A group of physicians from Denmark conducted a year-long study of the effectiveness of nicotine chewing gum in helping people stop smoking. The 113 people who participated in the study were all smokers. Of these, 60 were given a chewing gum with 2 mg of nicotine, and 53 were given a placebo chewing gum with no nicotine. This was a randomized controlled study. All were told to use the gum and refrain from smoking. Results showed that 23 of the smokers given the nicotine chewing gum had remained nonsmokers for the 1-year period while 12 of the smokers given the placebo had remained nonsmokers during the same period. Do these results support the conclusion that nicotine gum can help stop smoking? Test at α = 0.05.

1-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

In developing patient appointment schedules, a medical center wants to compare the mean time that staff members spend with patients between two offices--one in Cleveland and one in Cincinnati. A random sample of 30 office visits is taken from each office. Estimate the difference with a 95% level of confidence.

1-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost of delivery) = 0.728*(weight) + 5.49. If a package you want to ship weighs 13.753 ounces and the true cost of the shipment is $12.229, the residual is -3.273. Interpret this residual in terms of the problem.

Question 5 options:

A social scientist would like to analyze the relationship between educational attainments (years in higher ed) and annual salary (in $1,000s). He collects the data above.

a. What is the equation for predicting salary based on educational attainment?

b. What is the coefficient for education?

c. what is the predicted salary for someone with 4 years of higher ed?

A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 100 91 119 127 93 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1000 population for people over 50 93 109 100 97 110 88 110 79 115 100 89 114 85 96

(i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2 H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 > μ2; H1: μ1 = μ2

(b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (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 α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50. Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

The amount of beef produced on private farms in a particular country has changed over time. This table gives approximate values for the amount of beef produced for particular years in that country.

1.With linear regression, what is the value of the coefficient of determination (give the entire decimal)?

2. With quadratic regression, what is the value of the coefficient of determination (give the entire decimal)?

3. When making predictions that are within the original domain and range values of data from the table, which predictions would be 'best': when using linear regression OR when using quadratic regression?

In 1898, Hermon Bumpus studied a number of house sparrows that were brought to the Anatomical Laboratory of Brown University after an uncommonly severe winter storm. 35 birds survived and 24 perished.
In the spreadsheet, the weights of birds in grams (g) are given.
Is there a significant difference between the weights of the sparrows that perished and the weights of the sparrows that survived?
Using a t-test of independent samples (let alpha = 0.05), answer the following.

• t = ? df = ?

• Critical value of t = ? (hint: this is a two-tailed test)

• Should you reject the null hypothesis? (yes or no)

Suppose the sample mean forearm lengths for a randomly selected group of eleven men turns out to be 25. 5 cm with a corresponding standard deviation of 1. 52 cm. Find the 99% confidence interval for the true mean forearm 2 length of all men.

2) Refer to the last problem. Consider repeating the task of finding similar confidence intervals 4000 times (each of these 4000 intervals has the same confidence level of 99% and each interval is based on the same sample size eleven). Approximately how many of these intervals do you expect to include the true forearm length of all men? (Your answer must be given as an integer. Also note that there is no partial credit given for this problem).

4 fair coins are tossed. Let X be the number of heads and Y be the number of tails. Find Var(X-Y)

Solution: 3.5

Why?

x:4,5,3,6,10

y:4,6,5,7,7

A.)Determine .95 confidence interval for the mean perdicted when x =7

b.) Determine the .95 perdection interval for an indvidual predicted when x =7

Analysis of a random sample of 15 specimens of cold-rolled steel to determine yield strengths resulted in a sample mean strength of 29. 8 and a standard deviation of 4. 0. A second random sample of 14 specimens of galvanized steel resulted in a sample mean of 32. 7 and a standard deviation of 5. 0. Does the data indicate that the true mean yield strengths for the two given populations (cold-rolled or galvanized) are different? Test at a= 0. 01. Make sure to find/estimate the p-value.

1. Which subject had the highest rankings for relative peak power? Which subject had the lowest ranking? Provide an explanation as to why these individuals were the highest and lowest ranking?

2. Which subject had the highest rankings for relative mean power? Which subject had the lowest ranking? Provide an explanation as to why these individuals were the highest and lowest ranking?

The mean number of words per minute (WPM) read by sixth graders is 83 with a standard deviation of 12 WPM. If 89 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 1.4 WPM? Round your answer to four decimal places.