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Solving various questions on hypothesis testing

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______ 1. The variable about which the investigator wishes to make predictions or estimates is called the ____.
a. dependent variable b. unit of association
c. independent variable d. discrete variable

______ 2. In regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the _____.
a. coefficient of determination b. slope of the regression line
c. Y intercept of the regression line d. correlation coefficient

______ 3. In the equation y = b0 +b1 (x), b0 is the _____.
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient

______ 4. In the equation y = b0 + b1 (x), b1 is the _____.
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient

______ 5. In regression and correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the _____.
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient

______ 6. In regression and correlation analysis, the measure whose values are restricted to the range -1 to +1, inclusive, is the
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient

______ 7. The quantity is called the _______________ sum of square.
a. least b. explained
c. total d. unexplained

______ 8. If, in the regression model, b sub 1 = 0, we say there is _____________ linear relationship between X and Y.
a. an inverse b. a significant
c. a direct d. no
______ 9. If, in the regression model, b sub 1 is negative, we say there is _____________ linear relationship between X and Y.
a. an inverse b. a significant
c. a direct d. no

______ 10. If two variables are not related, we know that ________________.
a. their correlation coefficient is equal to zero.
b. the variability in one of them cannot be explained by the other.
c. the slope of the regression line for the two variables is equal to zero.
d. all of the above statements are true.

True or False
_______ 11. The usual objective of regression analysis is to predict estimate the value of one variable when the value of another variable is known.

_______ 12. Correlation analysis is concerned with measuring the strength of the relationship between two variables.

_______ 13. In the least squares model, the explained sum of squares is always smaller than the regression sum of squares.
_______ 14. The sample correlation coefficient and the sample slope will always have the same sign.

_______ 15. An important relationship in regression analysis is = .

_______ 16. If zero is contained in the 95% confidence interval for b, we may reject Ho: b = 0 at the 0.05 level of significance.

_______ 17. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r2 = 0.33.

_______ 18. In general, the smaller the dispersion of observed points about a fitted regression line, the larger the value of the coefficient of determination.

_______ 19. When small values of Y tend to be paired with small values of X, the relationship between X and Y is said to be inverse.

_______ 20. Other things are equal, decreasing α increases β.

The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) _____________________ concerning a (an) _____________________ by examining the data contained in a (an) _____________________ from that _____________________.
The _____________________ hypothesis is the hypothesis that is tested.
If the null hypothesis is not rejected, we conclude that the alternative __________________.
If the null hypothesis is not rejected, we conclude that the null hypothesis ______________.
A Type I error occurs when the investigator ______________________________________.
A Type II error occurs when the investigator ______________________________________.
Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.
Given, H0: µ= µ0, then Ha: ___________________________________.
Given H0: µ ≤ µ0, then Ha: ___________________________________.
Given H0: µ ≥ µ0, then Ha: ___________________________________.
When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of σ2, the test statistic is _________________.
When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with an unknown variance, the test statistic is _________________.
Given: H0: µ= 100; Ha: µ ≠ 100; α = 0.03; computed z = 2.25, p = 0.0244. The null hypothesis should reject because __________________________________________.
The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as____________ as or more _______ than that actually obtained is less than or equal to α, the null hypothesis is_______________. Otherwise, the null hypothesis is ______________________.
The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ______________ for the ________________test.

What is the null hypothesis?

What is the alternative hypothesis?

Explain the p-value.

Show 3 ways how to calculate r^2.

What is the importane of having a critical value?

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The solution gives detailed answers to various questions on hypothesis testing. All possible questions are included for this topic.

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6 Hypothesis Testing Questions

Problem 14.3
The marketing manager of a large supermarket chain would like to determine the effect of shelf space on the sales of pet food. A random sample of 12 equal-sized stores is selected, with the following results:

(see attachment for clearer tables)

Store Shelf Space X (Feet) Weekly Sales Y
(Hundreds of Dollars)
1 5 1.6
2 5 2.2
3 5 1.4
4 10 1.9
5 10 2.4
6 10 2.6
7 15 2.3
8 15 2.7
9 15 2.8
10 20 2.6
11 20 2.9
12 20 3.1

a. Set up a scatter diagram (NOTE: you can select this as an output with eth regression).
? ANSWER:

b. Assuming a linear relationship, use the least squares method to find the regression coefficients B0 & B1.
? ANSWER:

c. Interpret the meaning of slope (B1) in this problem.
? ANSWER:

d. Predict the average weekly sales (in hundreds of dollars) of pet food for stores with 8 feet of shelf space for pet food.
? ANSWER:

e. Suppose that sales in store 12 are 2.6. Repeat b-d with this value and compare the results to your original results.
? ANSWER:

f. How much shelf space would you recommend that the marketing manager allocate to pet food? Explain..
? ANSWER:

Problem 14.14
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Using the computer output you obtained to solve that problem.

a. Determine the coefficient of determination r2 and interpret its meaning.
? ANSWER:

b. Determine the standard error of the estimate.
? ANSWER:

c. How useful do you think this regression model is for predicting sales?
? ANSWER:

Problem 14.22
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Perform a residual analysis for these data. Based on the results obtained,

a. Determine the adequacy of fit of the model.
? ANSWER:

b. Evaluate whether the assumptions of regression have been seriously violated.
? ANSWER:

Problem 14.30
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales.

a. Is it necessary to compute the Durbin Watson statistic? Explain.
? ANSWER:

b. Under what circumstance would it be necessary to compute the Durbin Watson statistics before proceeding with the least squares method of regression analysis?
? ANSWER:

Problem 14.37
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Using the output you obtained to solve that problem.

a. At the .05 level of significance, is there evidence of a linear relationship between shelf space and sales?
? ANSWER:

Problem 14.51
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales.

a. Set up a 95% confidence interval estimate of the average weekly sales for all stores that have 8 feet of shelf space for pet food.
? ANSWER:

b. Set up a 95% confidence interval estimate of the average weekly sales of an individual store that has 8 feet of shelf space for pet food.
? ANSWER:

c. Explain the difference in the results obtained in a & b..
? ANSWER:

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