Hypothesis Test Problem Questions

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Explanation & Answer length: 26 Questions.

1. The level of significance indicates the probability of rejecting a true null hypothesis. True False

2. You can make a Type I error when the null hypothesis is correct. True False

3. The power of a statistical test is the probability of rejecting a false null hypothesis. True False

4. In a hypothesis test about Mean, increasing the level of significance from 0.05 to 0.10 will raise the chance of a Type II error; other relevant factors being held constant. True False

5. In a hypothesis test about Mean, switching the significance level from .05 to .10 will make type I error more likely; other relevant factors being held constant. True False

6. The larger is the gap between the hypothesized mean and the actual Mean, the stronger is “the power of the test.” True False

7. You cannot make a Type II error when the null hypothesis is correct. True False

8. A tire manufacturer has to find the average tensile strength of rubber in a particular tire brand. Assuming normality and a known population standard deviation, the manager uses a Z test to check that the mean tensile strength is 850 pounds per square inch. The calculated Z-value is a positive value that yields a p-value of 0.015. If the specified alpha is 0.01 is used, we reject the Null hypothesis. True False

9. The greater the p-value, the more we doubt the null hypothesis. True False

10. The average for a professional basketball player, who is retiring. is 21 points per game. There are several potential replacements. The owner believes that signing a replacement is only justified if one scores an average more than 22 points per game. We can represent this Hypothesis Test problem as: A) A. H0: μ ≤ 21 vs. H1: μ > 21 B) H0: μ ≤ 22 vs. H1: μ > 22 C) H0: μ ≥ 21 vs. H1: μ < 21 D) H0:μ ≥ 22 vs. H1: μ < 22

11. We are performing a “large sample” test of H0:: μ ≤ 10 vs. H1: μ > 10 with a critical value approach. The Null hypothesis will be rejected at significance level α if the absolute value of calculated test statistic is: A) Less than Zα/2 B) Less than Zα C) Greater than Za/2 D) Greater than Zα E) Less than the p-value

12. If we do not reject a null hypothesis at the 0.05 significance level, we will __ reject at the 0.10 level. A) Always B) Sometimes C) Never D) Cannot say without knowing one-tailed or two-tailed.

13. We are testing whether the average time employees stay with a company is less than three years, given that a randomly selected sample of 64 employees has a mean of 2.76 years and a standard deviation of 0.8 years. We assume a normal distribution. Our conclusion will be: A) Reject the Null at 5% significance level but not at 1% level. B) Reject the Null at 10% significance level but not at 5% level. C) Reject the Null even at 1% significance level D) Cannot reject the Null even at 10% significance level E) Reject the Null at 5% significance level but not at 10% level

14. In a large sample test as H0: μ =10 vs. Ha: μ ≠10, using a p-value approach, we reject H0 at the level of significance α when the p-value is: A) greater than α/2 B) greater than α C) less than α D) less than α/2 E) Less than Zα

15. If the sample size is less than 30 in a hypothesis test about population Mean with unknown population standard deviation, one compares the computed test statistic for significance with a value from the ___ distribution. A) t B) Z C) Binomial D) Hypergeometric E) Left-skewed.

16. In an early study, researchers at a private University found that 33% of the freshmen had received at least one A in their first semester. University administrators have received report that grade inflation may have caused this percentage to increase recently. A random sample of 500 freshmen found that 180 had at least one A in their first semester. Calculate the appropriate test statistic and test the hypotheses related to the concern and test at 5% and 1%. (Submit your answers through D2L in the Assignment section. You have to show your work or intermediate steps to get full points)

17. Suppose a study is conducted to investigate the relationship between the scores students receive on their Midterm and final tests. Based on the following sample, find the correlation coefficient : Mid Final 180 280 195 280 210 300 225 316 240 320 255 350 255 370 264 320 265 400 290 350 A) 0.566 B) 0.645 C) 0.738 D) 0.802 E) 0.905

18. The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable. True False

19. The following assumption about the error term is incorrect. A) Errors are normally distributed. B) The mean of error terms is zero. C) Error terms have a constant variance. D) Error terms depend on the explanatory variable. E) Error terms depend on the explanatory variable.

20. The Least Squares Regression minimizes the sum of A) deviations between actual and predicted Y values. B) squared deviations between actual and predicted X values. C) absolute deviations between actual and predicted Y values D) absolute deviations between actual and predicted X values E) squared deviations between actual and predicted Y values

21. The coefficient of Determination only indicates the strength of the relationship between the independent and dependent variables but does not reveal the direction of the relationship (positive or negative). True False

22. When using simple regression analysis, if there is a strong correlation between the independent and dependent variables, we can conclude that an increase in the value of the independent variable is associated with an increase in the value of the dependent variable. True False

23. The standard error of the estimate is the sample estimated standard deviation of the explanatory variable (X). True False

24. The sample estimate of the variance of error in a Regression model is A) MSE B) b0 C) b1 D) SSE E) SSxy

25. A merchant needs a forecast for the sales of a product (in millions). He thinks that the sale is affected by expenditure on advertising (in millions of dollars). Based on the data set with six observations, the summary statistics are given below (X is expense on advertising expenditure in million dollars and Y is number of products sold in millions): ∑X = 24; ∑Y = 42; ∑X2 = 124; ∑Y2 = 338; ∑XY = 196 Find the Intercept and slope, write the Regression Equation, and interpret the results. Make a forecast for the sale of products (in millions) if the advertising expenditure is 5 million dollars. Calculate the correlation coefficient, coefficient of Determination. Verify the relationship between the coefficient of correlation and the coefficient of Determination. Calculate SSE and MSE and standard error of the slope coefficient and perform the test of significance. (Submit your answers through D2L in the Assignment section. You have to show your work or intermediate steps to get full points)

26. A product rating agency has the following data about the quality score for an electronic product and respective prices for 10 popular brands. Brand Price Score A 2900 55 B 2800 54 C 2700 45 D 3500 56 E 3300 54 F 2000 35 G 4200 68 H 3100 56 I 2500 32 J 3000 45 Calculate the Regression coefficients based on the above data and explain what the values indicate. Measure the Goodness of Fit using the Coefficient of Determination and interpret the calculated value with respect to the model’s overall explanatory power. Also check the relationship between R2 and r. (Submit your answers through D2L in the Assignment section. You have to show your work or intermediate steps to get full points)

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