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# Hypothesis Testing & Regression Analysis

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7 statistic questions (.doc)
Formulas and Tables (for reference)

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HYPOTHESIS TESTING
Problem 1 thru 4 (don't forget to state your hypotheses, type of test, alpha level, and your decision statistic; draw a bell curve diagram indicating rejection region)

PROBLEM 1: Conduct a one-tailed hypothesis test given the information below.

A certain brand of Green Energy light bulbs was advertised as having an average illumination life-span of 2,500 hours. A random sample of 50 bulbs burned out with a mean life-span of 2,470 hours and a sample standard deviation of 140 hours. With a 0.05 level of significance, is the sample mean less than the advertised mean?

PROBLEM 2: Given the following data from two independent samples, conduct a one-tailed hypothesis test to determine if the first sample mean is larger than the second sample mean, given a 0.05 level of significance.

n1 = 55 n2 = 46
xbar1= 72 xbar2 = 62
s1=15 s2 = 12

PROBLEM 3. Conduct a one-tailed hypothesis test given the information below.

A test was conducted to determine whether gender of a spokesperson affected the likelihood that consumers would prefer a new vacuum cleaner. A survey of consumers at a trade show employing a female spokesperson determined that 78 out of 200 customers preferred the product, while 56 of 180 customers preferred the product when a male spokesperson was employed. At the 0.05 level of significance, do the samples provide sufficient evidence to indicate that on the average, fewer consumers prefer a new product when the spokesperson is male?

PROBLEM 4. Conduct a two-tailed hypothesis test given the information below.

Assuming that the population variances are equal for male and female Grade Point Averages (GPAs), use the following sample data to test whether the averages are different at the 0.05 level of significance.

Male GPA's Female GPA's
Sample Size 17 15
Sample Mean 3.8 3.95
Sample Standard Dev .5 .7

PROBLEM 5. Regression Analysis (a-e)

A real estate investor has devised a model to estimate home prices in a new suburban development. Data for a random sample of 30 homes were gathered on the selling price of the home (in units of \$1,000), the home size (square feet), the lot size (in units of 1,000 square feet), and the number of bedrooms.

The following multiple regression output was generated:

Regression Statistics
Multiple R 0.9647
R Square 0.9307
Standard Error 26.0389
Observations 30

Coefficients Standard Error t Stat P-value
Intercept -34.6165 38.3735 -0.9021 0.3753
X1 (Square Feet) 0.1532 0.0184 8.3122 0.0000
X2 (Lot Size) 9.0024 1.7120 5.2583 0.0002
X3 (Bedrooms) 17.3903 6.8905 2.5238 0.1259

a. Why is the coefficient for lot size a positive number?

b. Which is the most statistically significant variable? What evidence shows this?

c. Which is the least statistically significant variable? What evidence shows this?

d. For a 0.05 level of significance, should any variable be dropped from this model? Why or why not?

e. Predict the sales price of a 2134-square-foot home with a lot size of 13,400 square feet and three bedrooms.

Problem 6: Hypothesis Testing

True/False Questions

a. If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

True False

b. If we are testing for the difference between two population proportions, it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

True False

c.If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the standard deviations are pooled to compute the best estimated variance.

True False

Multiple Choice Questions

d. If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternate hypothesis and rejection region?

Problem 7: Define multicollinearity in the following terms:

a. In which type of regression is it likely to occur?

b. What is the negative impact of multicollinearity in a regression?

c. Which method is used to determine if it exists?

d. If multicollinearity is found in a regression, how is it eliminated?