Hiroshi Sato, an owner of a sushi restaurant in San Francisco, has been following an aggressive marketing campaign to thwart the effect of rising unemployment rates on business. He used monthly data on sales ($1,000s), advertising costs ($), and the unemployment rate (%) from January 2008 to May 2009 to estimate the following sample regression equation: Salesˆt = 12.43 + 0.02Advertising Costst−1 − 0.52Unemployment Ratet−1. a. Hiroshi had budgeted $540 toward advertising costs in May 2009. Make a forecast for Sales for June 2009 if the unemployment rate in May 2009 was 8%. (Enter your answer in dollars not in thousands.) Salesˆt $ 23.22 23.22 Incorrect b. What will be the forecast if he raises his advertisement budget to $640? (Enter your answer in dollars not in thousands.) Salesˆt $ 21.07 21.07 Incorrect c. Reevaluate the above forecasts if the unemployment rate was 8.6% in May 2009. (Enter your answers in dollars not in thousands.) Advertising Salesˆ t 540 $ 31.96 31.96 Incorrect 640 $ 20.75 20.75 Incorrect

With regard to regression models, which of the following statements is correct?

i) Linear restrictions on regression parameters cannot be tested using an F-test.

ii) The general-to-specific approach (also called “top-down”) starts with a model containing all explanatory variables. Subsequently, the least significant variables are dropped one by one until all of the variables remaining in the model are statistically significant.

iii) Multicollinearity in a regression results in high t-statistics for individualexplanatory variables and a failure of the F-test to reject the null hypothesis that the explanatory variables are jointly insignificant.

People were polled on how many books the read the previous year. Initial survey results indicate that s=11.6 books.

(a) How many subjects are needed to estimate the mean number of books read the previous year within four books with 95% ​confidence?

(b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95​% confidence?

(c) How many subjects are needed to estimate the mean number of books read the previous year within four books with 99​% ​confidence?

Answer these parts to Objective number A

2. What is the single most important advantage of the median as a measure of location?

A. not affected by extreme outliers

B. statistically efficient

C. don’t have to know all individual values in order to calculate it

D. always an observable value

E. more than one of the above

3. The Graco Distribution Center in Rogers MN has automated storage/retrieval lanes for much of their inventory. An audit of inventory is conducted weekly for inventory counts. The results for a random sample of 8 inventory counts found the following number of inventory discrepancies; 9, 67, 19, 8, 18, 8, 15, 8. Based on the data, which measure of variability would you place most weight on?
A. median
B. InterQuartile Range
C. standard deviation
D. range

E. coefficient of variation

4. The Graco Distribution Center in Rogers MN has automated storage/retrieval lanes for much of their inventory. An audit of inventory is conducted weekly for inventory counts. The results for a random sample of 8 inventory counts found the following number of inventory discrepancies;   9, 67, 19, 8, 18, 8, 15, 8. Find the median.
A. 8
B. 12
C. 18
D. 37.5

E. none of the above

5. The Graco Distribution Center in Rogers MN has automated storage/retrieval lanes for much of their inventory. An audit of inventory is conducted weekly for inventory counts. The results for a random sample of 8 inventory counts found the following number of inventory discrepancies;   9, 67, 19, 8, 18, 8, 15, 8. Find the standard deviation.
A. 18.00
B. 397.71
C. 24.50
D. 19.94

E. none of the above

6. Edina Reality is interested in drawing comparison on price variations between two neighborhoods Woodbury and Cottage Grove. Woodbury has x-bar of 120,000$ and a sample standard deviation of 2000$. Cottage grove has x-bar of 900,000$ and sample standard deviation of 10,000$. Which neighborhood has higher relative variability?

1. Woodbury has higher relative variability as compared to Cottage Grove.
2. Cottage Grove has higher relative variability as compared to Woodbury.
3. Both neighborhoods have same variability.
4. Cannot decide based on given information.

Question 4

Which of the following time sequence is a weak stationary? Justify your answer!

• zt =at,whereat ∼i.i.d.(0,1)forallt∈R.
• zt =t+at,whereat ∼i.i.d.(0,1)forallt∈R.
• zt = A sin(t + B), where A is a random variable with a zero mean and a unit variance and B is a random variable with a Uniform distribution (−π, π) independent of A. Hint: You may need to use the trigonometric formula 2 sin A sin B = cos(A − B) − cos(A + B) and others. You may also need to use the mean and the variance of Uniform random variable.

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a sample variance of S2 = 16. A 95% confidence interval estimate for the population variance of service times for all their new automobiles is: A. 8.576 to 39.794 B. 4.162 to 16.324 C. 4.126 to 15.760 D. 2.928 to 6.308  

Dr. Anderson is a mammalogist who studies deer mice. He is trying to improve his success in trapping female deer mice. He conducts a study where he uses peanut butter vs. nutella as bait in his traps. The data he collects is shown in the table below. He is going to use a Chi-Squared test to analyze his results.

Dr. Anderson is a mammalogist who studies deer mice. He is trying to improve his success in trapping female deer mice. He conducts a study where he uses peanut butter vs. nutella as bait in his traps. The data he collects is shown in the table below. He is going to use a Chi-Squared test to analyze his results.

(a)  Females prefers peanut butter bait over nutella or vice versa would be the   (null or alternate) hypothesis

(b) The expected frequency for females that prefer peanut butter is  (report to 4 decimal places)

(c)   The expected frequency for females that prefer nutella is  (report to 4 decimal places)

(d) The expected frequency for males that prefer peanut butteris  (report to 4 decimal places)

(e) The expected frequency for males that prefer nutella is  (report to 4 decimal places)

(f) degrees of freedom =

(g) The calculated chi-square value =  (report to 4 decimal places)

(i) The critical chi-square value at alpha =0.05 =

(j) Would you reject or fail to reject the null hypothesis?

(k) Would females prefer one type of bait than the other?  (yes or no)

The weights of kittens have a symmetric shape with mean of 3.6 pounds and a standard deviation of 0.4 pounds, answer each of the following:

a. What percent of kittens weigh between 2.8 and 4.8 pounds?

b. Which weight represents ?84.

What is different about what the sign of a correlation (negative or positive) tells us vs. the magnitude of the correlation coefficient (i.e. how much r is greater than or less than zero)?

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the critical value method or the P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 693 708 887 849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the critical value method or the P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below. 14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2 Test the claim at the 0.01 significance level.

A library system lends books for periods of 21 days. This policy is being reevaluated in view of a possible new loan period that could either lengthen or shorten the 21-day period. To aid in this decision, book-lending records were consulted to determine the loan periods actually used by the patrons. A random sample of eight records revealed that following loan periods in days: 21, 15, 12, 24, 20, 21, 13, and 16. Do the actual loan periods differ from 21 days?

a. State your null and alternative hypothesis.
b. Conduct the appropriate test and state your conclusion. c. What is the 95% confidence interval? (If applicable)

Let X1, X2, ..., Xn be a random sample from Exp(?). Find the MVUE of the median of this exponential distribution.

A.)Test whether mu 1μ >mu 2 at the alpha equals=0.05 level of significance for the given sample data.

Find the P value

Find the test statistical  for the hypothesis

Find the lower and upper bound

B.) Construct a 99​% confidence interval about mu μ1−μ2.

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 35.9 and 2.5 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 37 mpg?

b. What is the probability that the average mpg of three randomly selected passenger cars is more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)