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1.7 Based on the data for the years 1962 to 1977 for the United States, Dale Bails and Larry Peppers17 obtained the following demand function for automobiles:

Yt = 5807 + 3.24Xt r2 = 0.22

Se = (1.634)

Where Y = retail sales of passenger cars (thousands) and X = the real disposable income (billions of 1972 dollars).
Note: The se for b1 is not given.
a. Establish a 95% confidence interval for B2.
b. Test the hypothesis that this interval includes B2 = 0. If not, would you accept this null hypothesis?
c. Compute the t value under H0: B2 = 0. Is it statistically significant at the 5 percent level? Which t test do you use, one tailed or two tailed, and why?

2.7 The characteristic line of modern investment analysis involves running the following regression:

rt = B1 + B2r mt + ut

where r = the rate of return on a stock or security
rm = the rate of return on the market portfolio represented by a broad market index such as S&P 500, and
t = tine

In investment analysis, B2 is known as the beta coefficient of the security and is used as a measure of market risk, that is, how developments in the market affect the forunes of a given company.

Based on 240 monthly rates of return for the period 1956 to 1976, Fogler and Ganapathy obtained the following results for IBM stock. The market index used by the authors is the market portfolio index developed at the University of Chicago.

rt = 0.7264 = 1.0598r mt

se = (0.3001) (0.0728) r2 = 0.4710

a. Interpret the estimated intercept and slope.
b. How would you interpret r2?
c. A security whose beta coefficient is greater than 1 is called a volatile or aggressive security. Set up the appropriate null and alternative hypothesis and test them using the t test. Note: Use a =5

Assume that in a hypothesis test with null hypothesis H 0: mu = 14.0 at alpha = 0.05, that a value of 13.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidenceinterval result of:
a) the 95% confidenceinterval for the mean contains the value 14.0
b) the 95% confidenceinterval

Assume that in a hypothesis test with null hypothesis = 13.0 at 0.05, that a value of 11.0 for the sample mean results in the null hypothesis not being rejected. That corresponds to a confidenceinterval result of
A. The 95% confidenceinterval for the mean does not contain the value 13.0
B. The 95% confidenceinterval for

Which of the following is not needed to be known to calculate a confidenceinterval?
a. standard deviation
b. sample size
c. mean
d. degree of confidence

A confidenceinterval for the population mean tells us which values of mean are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis. Ho:mean =Mo starting with a confidence interva

1. What are the null and alternate hypotheses for this test? Why?
2. What is the critical value for this hypothesis test using a 5% significance level?
3. Calculate the test statistic and the p-value using a 5% significance level.
4. State the decision for this test.
5. Determine the confidenceinterval level that would be a

Exercise 8.5
Find a confidenceinterval for u assuming that each sample is from a normal population.
a. x = 14, sigma = 4, n = 5, 90 percent confidence
b. x = 37, sigma = 15, 99 percent confidence
c. x = 121, sigma = 15, 95 percent confidence
Exercise 9.19
Calculate the test statistic and p-value for each sample.

A quality control engineer wanted to estimate the mean weight (in grams) of M&M candies being produced on a certain machine in the factory. After collecting an appropriate random sample of M&M candies, he obtained the following weights:
.81 .86 .85 .79 .98 .84
.9 .87 .77 .82 .86 .87
.87 .88 .94 .86 .96 .82
.88 .98 .75 .

Consider the following Hypothesis Testing:
H0: δ1² = δ2²
Ha: δ1² ≠ δ2²
The sample size for sample 1 is 25, and for sample 2 are 21. The variance for sample 1 is 4.0 and for sample 2 is 8.2
a) at the confidence level of 0.98, what is your conclusion of this test?
b) What is the confidence