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Statistics homework help
Stat 216 – Assignment 3 Due Friday 5:30 pm June 12, 2020 NOTES: Answer ONLY will be NO credits. No R program calculations. Statistical Tables ONLY
Two samples of the starting annual salaries (in thousands of dollars) of females and males in a certain industry were collected. The sample of starting salaries of females yielded n1 = 5, x1 = 43.9, and s1 = 5.4. The sample of starting salaries of males yielded n2 = 7, x2 = 42.8, and s2 = 2.7. Let µ1 and µ2 denote the true mean salaries of the two populations (female and male starting salaries). Construct a 98% confidence interval for µ1 − µ2.
It has been estimated that, on average, a family of four in Canada spends about $1135 annually on dental expenditures. Suppose that the dental association in a particular region wants to determine if this figure is accurate for their area of the country. To test this, 22 families of four are randomly selected from the population in the area and a log is kept of each family’s dental expenditures for one year. The average for the sample was then calculated to be $1031, with a standard deviation of $240. Assuming that dental expenditures are normally distributed, the dental association wants to conduct a hypothesis test to determine whether it can infer that average dental expenditures in the region differ from that of the country at α = .05
A large manufacturing company investigated the service it received from suppliers and discov- ered that, in the past, 32% of all supply shipments were received late. However, the company recently installed a system in which suppliers are linked more closely to the manufacturing process. A random sample of 118 deliveries since the system was installed revealed that 22 deliveries were received late.
The company wants to use the sample to test whether the proportion of late deliveries was reduced by the new system. What is the observed value of the appropriate test statistic?
1
161 people who visited one hospital’s emergency room in a 6-month study period with injuries from in-line skating were interviewed. The interviewer found that 53 people were wearing wrist guards and 6 of them had wrist injuries. Of the 108 who did not wear wrist guards, 45 had wrist injuries. We are interested in the difference between the proportions of wrist injuries in the population wearing wrist guard and the population without. Find 95% confidence interval.
An Italian restaurant close to a university campus contemplated changing their recipe for pizza sauce. A random sample of eight students was chosen, and each was asked to rate on a scale from 1 to 10 how they liked the original sauce and the proposed new one. The scores of the taste comparison are shown in the given table. Higher numbers indicate a greater liking of the product.
Student S1 S2 S3 S4 S5 S6 S7 S8
Original Sauce Rating 6 4 5 8 3 6 7 5 New Sauce Rating 8 9 4 7 9 9 7 9
To test the hypothesis that students prefer the new pizza sauce over the original sauce, what is the observed value of the appropriate test statistic that should be used?
A particular city would like to put information on their tourism website to give travellers an idea of how much they should expect to pay per night for a hotel room. A random sample of 10 popular hotels in the city center produced an average rate of $220, with a standard deviation of $17. A second random sample was taken of 15 hotels outside the city center, but within 5 km of the city, and this sample had an average rate of $139, with a standard deviation of $14. Find the upper bound of a 95% confidence interval for the amount that the average hotel rate within the city center exceeds the average rate for hotels within 5 km. Assume the populations are approximately normal.
2
A marketing consultant is studying the monthly entertainment expenses of single men and women, and believes that single men spend more on entertainment than do single women. To study her belief, she takes a random sample of single men and women and determines their monthly entertainment expenses. The summary statistics are: n1 = 5, x1 = $305, s1 = $87, n2 = 7, x2 = $220, and s2 = $60, where population 1 is single men and population 2 is single women. Assuming both populations are normal, what is the number of degrees of freedom of the test statistic that should be used to test her belief?
Questions 8 and 9 refer to the following setup.
The manager of a car dealership believes there is a relationship between the number of salespeople on duty and the number of cars sold. For five weeks he recorded the number of people on duty and how many cars were sold:
Week Number of Salespeople, x Number of Cars Sold, y
1 6 79 2 6 64 3 4 49 4 2 23 5 3 52
The manager then used simple linear regression to calculate the line ŷ = 9.23+10.52x, where s2x = 3.2, s
2 y = 428.3, sxy = 33.65, and SSE = 297.8.
What proportion of the variation in y is explained by the variation in x?
The manager wants to test his hypothesis that there is a positive linear relationship between the number of salespeople on duty and the number of cars sold, using the slope of the linear regression line he found. What is the observed value of the test statistic that should be used?
3
Investment analysts generally believe that the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when lending rates are up.
(a) Use the following data to construct a least squares regression line to predict the bond rates based on the prime interest rate.
Prime Interest Rate (in %) 16 6 8 4 7
Bond Rate (in %) 5 12 9 15 7
You can use the fact that for the given data, ∑ xi = 41,
∑ yi = 48,
∑ x2i = 421,∑
y2i = 524, and ∑ xiyi = 333.
(b) What is the residual at the point (8, 9)?
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