Reference no: EM132152775

Question 1 - In a simple regression analysis, if the coefficient of determination is 0.93, this means that:

93% of the variation in y can be explained by the variation in x.

93% of the y values are positive.

93% of the x values are equal.

93% prediction of y is correct.

Question 2 - An online seller of computer monitor offers a one-year (12 months) warranty on its monitors because she believes that if the monitor is faulty, it will fail within this time period. Suppose that a random sample of 25 monitors that failed have the mean time to failure from purchase as 13.5 months. Assuming the time to failure follows normal distribution with known standard deviation of σ = 3.1 months, the p-value associated with testing H₀: μ = 12 and H_A: μ > 12 is

0.9922

0.0000

0.0078

0.078.

Question 3 - A regression analysis was performed by regressing Y = weekly expenditures on food (in dollars) on X = weekly income (in dollars). The following results were obtained.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.58159
R Square	0.33825
Adjusted R Square	0.31374
Standard Error	97.18469
Observations	29

ANOVA

	df	SS	MS	F	Significance F
Regression	1	130348.1029	130348.1029	13.8009	0.0009
Residual	27	255011.3454	9444.8646
Total	28	385359.4483

 

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	140.1219	48.6255	2.8817	0.0077	40.3506	239.8932
X	0.6485	0.1746	3.7150	0.0009	0.2903	1.0067

The interpretation of R² = 0.3383 is;

If weekly income increases by $1, weekly expenditures on food would increase by $0.3383.

33.83% of variation in weekly food expenditures in explained by weekly income.

Weekly food expenditures and weekly income are not related to each other.

There is a positive correlation between weekly food expenditures and weekly income.

Question 4 - To test the overall significance of a multiple regression model

Y = β₀ + β₁X₁+ β₂X₂ + β₃X₃ + β₄X₄ +β₅X₅ +β₆X₆ + ε

with 6 independent variables and 87 observations, the numbers of degrees of freedom for the numerator and denominator, respectively, for the critical value of F are:

7 and 80

6 and 81

6 and 80

7 and 81

Question 5 - In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true then we say that:

a. a Type-I error is committed.

b. a Type-II error is committed.

c. a correct decision is made.

d. a two-tail test should be used instead of a one-tail test.

Question 6 - A regression analysis between quantity demanded (y in kg ) and price (x in dollars) of apples resulted in the equation y = 28 - 3x. The estimated regression equation implies that:

If price increases by $1, the demand is expected to decrease by 28 units.

If price increases by $1, the demand is expected to decrease by 3 units.

If price increases by $1, the demand is expected to increase by 28 units.

If price increases by $1, the demand is expected to increase by 3 units.

Question 7 - Two independent samples of sizes 30 and 35 are randomly selected from two normal populations with equal but unknown variances. Which of the following is the test statistic that should be used to test the difference between the population means?

Student t with 35 degrees of freedom.

Student t with 64 degrees of freedom.

F-test with any degrees of freedom

Z

Question 8 - The p-value criterion for hypothesis testing is to reject the null hypothesis if

a. p-value > 0.05.

b. p-value < α.

c. p-value > α

d. p-value = α.

Question 9 - A regression analysis between quantity demanded (y) and price (x) of potatoes resulted in the equation y = 42 - 3x. At what price will the consumers estimated demand be 27 units of the good?

$5.

$39.

$42.

$9.

Question 10 - Which of the following statements is true about correlation coefficient?

If the correlation coefficient is -1, it implies that there is a perfect positive linear relationship between two variables.

If the correlation coefficient is 1, it implies that there is a nonlinear relationship between two variables.

If the correlation coefficient is -1, it implies that there is a weak negative linear relationship between two variables.

If the correlation coefficient is 1, it implies that there is a perfect positive linear relationship between two variables.

Question 11 - In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows:

n₁ = 25, X^-₁ = 7.30, s₁ = 1.05.

n₂ = 20, X^-₂ = 6.80, s₂ = 1.50.

Assume that the population variances are unequal. Then the standard error of the sampling distribution of the sample mean difference is equal to:

0.3328.

0.3957.

0.5944.

0.2917.

Question 12 - An analyst randomly selects some fuel stations in Melbourne and Sydney to compare average fuel prices in both cities. This would be an example of:

independent samples only if the sample sizes are equal.

dependent samples.

dependent samples only if the sample sizes are equal.

independent samples.

Question 13 - Which of the following test statistics may be used to test a value of the population mean with unknown population variance given the small sample?

z-test or a t-test.

t-test.

z-test.

F-test

Question 14 - To test the difference between the means, two independent samples each with size less than 30 are drawn from normal populations. If the population variances are unknown and unequal, then the sampling distribution of the resulting test statistic would be:

Student t.

normal.

F-distribution

approximately normal.

Question 15 - Statisticians can translate p-values into several descriptive terms. Which of the following statement(s) is (are) correct?

a. If 0.05 < p-value ≤ 0.10, there is weak evidence to infer that the alternative hypothesis is true.

b. If 0.01 < p-value ≤ 0.05, there is strong evidence to infer that the alternative hypothesis is true.

c. If p-value < 0.01, there is overwhelming evidence to infer that the alternative hypothesis is true.

d. All the three statements are correct.

Question 16 - How earnings are related to experience and qualification?

It is well known that people with higher level of education earn more money whilst experience also contributes positively to earnings. To verify this, a random sample of 40 workers is chosen with information about their annual income, years of schooling, and years of experience. The model to be estimated is

Inc_i = β₀ + β₁ Edu_i + β₂ Exper_i + ε_i, i = 1,2,...,40

where,

Inc = Annual income,

Edu = Years of schooling,

Exper = Years of experience, and

i = ith worker in the sample.

Find the following missing values.

1. The value of the coefficient of determination?

2. The value of F-statistic?

3. To test the null of β_Edu = 5000 using the 95% confidence interval for the coefficient of education, our decision is.

4. Predicted value of annual earnings of an individual with 16 years of education and 8 years of experience is.

5. p-value of the test of overall goodness of fit is.

Question 17 - An estimated multiple regression model has the form y = 1.8 + 3.4x₁ + 1.5x₂ + 0.45x₃. As x₁ increases by 1 unit, with x₂ and x₃ held constant, the value of y, on average, is estimated to:

decrease by 3.4%.

decrease by 3.4 units.

increase by 3.4%.

increase by 3.4 units.

Question 18 - Two samples of sizes 37 and 45 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom of the equal-variances t-test statistic are:

84.

80.

85.

34.