# Hypothesis Test and SPSS Interpretation

Please try to include the following three elements for each of the question:

? Hypotheses (both null and alternative hypotheses)

? Analysis (Relevant SPSS printouts or Excel)

? Conclusion (interpretation of data)

? Do not need to outline and examine the assumptions that the chosen statistical technique makes (e.g., the distributions have equal variance in a multiple regression analysis) UNLESS stated in question/problem)

1. SPSS computation and Interpretation: The Asian economy faltered during the last few months of 1997. Investors anticipated that the downturn in the Asian economy would have a negative effect on the earnings of companies in the United States during the fourth quarter of 1997. The following sample data show the earnings per share for the fourth quarter of 1996 and the fourth quarter of 1997 (The Wall Street Journal, January 28, 1998).

a. Formulate H0 and H1 such that rejection of H0 leads to the conclusion that the mean earnings per share for the fourth quarter of 1997 are less than for the fourth quarter of 1996.

b. Use the data in the following table to conduct the hypothesis test. At alpha = 0.10, what is your conclusion?

Company Earnings 1996 Earnings 1997

Atlantic Richfield 1.16 1.17

Balchem Corp. 0.16 0.13

Black & Decker Corp. 0.97 1.02

Dial Corp. 0.18 0.23

DSC Communications 0.15 -0.32

Eastman Chemical 0.77 0.36

Excel Communications 0.28 -0.14

Federal Signal 0.40 0.29

Ford Motor Company 0.97 1.45

GTE Corp 0.81 0.73

ITT Industries 0.59 0.60

Kimberly-Clark 0.61 -0.27

Minnesota Mining & Mfr. 0.91 0.89

Procter & Gamble 0.63 0.71

2. SPSS computation and Interpretation:

A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data.

Factor B

Level 1 Level 2 Level 3

Factor A Level 1 135 90 75

165 66 93

Level 2 125 127 120

95 105 136

a. Formulate the appropriate pairs of H0 and H1 (There are more than one pair of hypotheses in this factorial experiment problem)

b. Construct the ANOVA table - no manual calculation and/or "interpretation" are required for 2(b). Please help show me the manual calculation in addition to computer-generated ANOVA table.

c. Test for the interaction effect as well as main effects (no hypotheses necessary, should be in 2a). Use alpha = .05.

3. SPSS computation and Interpretation: Barron's conducts an annual review of online brokers, including both brokers that can be accessed via a Web browser, as well as direct-access brokers that connect customers directly with the broker's network server. Each broker's offerings and performance are evaluated in six areas, using a point value of 0-5 in each category. The results are weighted to obtain an overall score and a final star rating, ranging from zero to five starts, is assigned to each broker. Trade execution, ease of use, and range of offerings are three of the areas evaluated. A point value of 5 in the trade execution area means the order entry and execution process flowed easily from one step to the next. A value of 5 in the ease of use area means that the site was easy to use and can be tailored to show what the user wants to see. A value of 5 in the range offerings area means that all of the investment transactions can be executed online. The following data show the point values for trade execution, ease of use, range of offerings, and the star rating for a sample of 10 of the online brokers that Barron's evaluated (Barron's, March 10, 2003). Use alpha = .05.

Broker Trade Execution Use Range Rating

Wall St. Access 3.7 4.5 4.8 4.0

E*TRADE (Power) 3.4 3.0 4.2 3.5

E*TRADE (Standard) 2.5 4.0 4.0 3.5

Preferred Trade 4.8 3.7 3.4 3.5

my Track 4.0 3.5 3.2 3.5

TD Waterhouse 3.0 3.0 4.6 3.5

Brown & Co. 2.7 2.5 3.3 3.0

Brokerage America 1.7 3.5 3.1 3.0

Merrill Lynch Direct 2.2 2.7 3.0 2.5

Strong Funds 1.4 3.6 2.5 2.0

(a) Determine the estimated regression equation that can be used to predict the start rating given the point values for execution, ease of use, and range of offerings (keep all three independent variables in your regression model even if you find some independent variable(s) that is/are NOT statistically significant). Briefly interpret answer.

(b) Use the F test to determine the overall significance of the relationship. What is the conclusion at the .05 level of significance? Need the relevant hypotheses before trying SPSS analysis.

(c) Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance? Need the relevant hypotheses before trying SPSS analysis.

***See attached file for full problem description.***

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#### Solution Preview

Please try to include the following three elements for each of the question:

? Hypotheses (both null and alternative hypotheses)

? Analysis (Relevant SPSS printouts or Excel)

? Conclusion (interpretation of data)

? Do not need to outline and examine the assumptions that the chosen statistical technique makes (e.g., the distributions have equal variance in a multiple regression analysis) UNLESS stated in question/problem)

1. SPSS computation and Interpretation: The Asian economy faltered during the last few months of 1997. Investors anticipated that the downturn in the Asian economy would have a negative effect on the earnings of companies in the United States during the fourth quarter of 1997. The following sample data show the earnings per share for the fourth quarter of 1996 and the fourth quarter of 1997 (The Wall Street Journal, January 28, 1998).

a. Formulate H0 and H1 such that rejection of H0 leads to the conclusion that the mean earnings per share for the fourth quarter of 1997 are less than for the fourth quarter of 1996.

Null hypothesis (H0) = mean earnings for 1997 are greater than or equal to the mean earnings for 1996

Alternative hypothesis (H1) = mean earnings for 1997 are less than the mean earnings for 1996

Notice that this is a one-sided test because we're testing if one mean is less than another, instead of if the two means are not equal to each other.

b. Use the data in the following table to conduct the hypothesis test. At alpha = 0.10, what is your conclusion?

Company Earnings 1996 Earnings 1997

Atlantic Richfield 1.16 1.17

Balchem Corp. 0.16 0.13

Black & Decker Corp. 0.97 1.02

Dial Corp. 0.18 0.23

DSC Communications 0.15 -0.32

Eastman Chemical 0.77 0.36

Excel Communications 0.28 -0.14

Federal Signal 0.40 0.29

Ford Motor Company 0.97 1.45

GTE Corp 0.81 0.73

ITT Industries 0.59 0.60

Kimberly-Clark 0.61 -0.27

Minnesota Mining & Mfr. 0.91 0.89

Procter & Gamble 0.63 0.71

We already decided that this would be a one-sided test. Looking at the data, it will be a t-test (because we don't know the population standard deviations) and it will be a matched-pairs test (paired-samples test), because each row of the data comes from one company - the two samples are NOT independent as they would be in a two-sample t-test.

I put the numerical data into two columns of an SPSS spreadsheet, and called the columns e_1996 and e_1997. I then went to analyze → compare means → paired samples t-test, and selected both variable names to go into the "paired variables" box. The results of the test are below:

The mean difference between the 1996 and 1997 earnings is 0.1243 with a 95% confidence interval of the difference of (-0.0642, 0.3128). The two-sided p-value is p = 0.178, which gives us a one-sided p-value of p = 0.089. This is low enough to reject the null ...

#### Solution Summary

The solution includes complete explanations for three statistics problems. These problems involve hypothesis testing, t-tests, confidence intervals, and ANOVA. Explanations of how to do the analyses in SPSS are provided. An explanation of how to do ANOVA by hand is also provided.

Statistics SPSS computation and interpretation

Cooling method for gas turbines. During periods of high electricit demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power. One measure of performance is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines, saved in the GASTURBINE file, are listed in the table. Suppose that a standard gas turbine has, on average, a heat rate of 10,000 kJ/kWh. Conduct a test to determine if the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10,000 kJ/kWh. Use α= .05. In addition, use the Shapiro-Wilk test to examine the normality hypothesis. (You don't have to draw the Q-Q plot). Show all work.

Data is given in the attachment.

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