Eco 302: Fall-20-Assignment 2: Chapters: 8, 9, 10, and 13: Total 250 points due by Midnight (11:59 pm), Sunday, Nov 29th, 2020
True/False Questions carry 2 points each, Multiple Choices carry 4 points each and the Essay type questions carry 10 points each: total 250 points.
True / False Questions (2 points each) Chapter 8 1. The sampling distribution of must be a normal distribution.
2. The reason sample variance has a divisor of n-1 rather than n is that it makes the sample variance an unbiased estimate of the population standard deviation.
3. The standard deviation of the sampling distribution of the sample mean increases as the sample size increases.
4. If a population is known to be normally distributed, then it follows that the sample mean must equal the population mean. 5. If the sampled population is a normal distribution, then the sampling distribution of must be normal for large samples but may not be normal for a small sample.
6. The mean of the sampling distribution of (X-bar) is not always equal to the mean of the sampled population. Chapter 9 7. Assuming the same level of significance , as the sample size increases, the value of t/2 approaches the value of z/2.
8. When constructing a confidence interval for a sample proportion, the t distribution is more appropriate (theoretically) whenever the population standard deviation is not known, whether the sample size is large or small.
9. When the level of confidence and sample proportion p remain the same, a confidence interval for a population proportion p based on a sample of n = 200 will be narrower than a confidence interval for p based on a sample of n = 100.
10. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be narrower, when the sample standard deviation s is larger than when s is smaller.
Chapter 10 11. The further the hypothesized mean is from the actual mean the greater the power of the test. 12. The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. She knows the population standard deviation and uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .01, the null hypothesis would be rejected. Assume that the population of pressure values is normally distributed.
13. The larger the p-value, the more we doubt the null hypothesis. 14. You cannot make a Type II error when the null hypothesis is true. 15. A Type II error is rejecting a true null hypothesis.
16. When conducting a hypothesis test about a single mean, other relevant factors held constant, changing the level of significance from .05 to .10 will increase the probability of a Type I error.
17. When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type II error.
18. The Alternative hypothesis sometimes includes an equal (=) sign.
19. When the null hypothesis is true, there is no possibility of making a Type II error. Chapter 13 20. The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.
21. The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
22. The slope of the simple linear regression equation represents the average change in the value of the independent variable (X) per unit change in the dependent variable (Y).
23. A significant positive correlation between X and Y does imply that changes in X cause Y to change.
24. The Coefficient of Determination is the ratio of explained variation to total variation.
25. When using simple regression analysis, if there is a strong correlation between the independent and dependent variable, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.
Multiple Choices (4 Points Each) Chapter 8 1. If the sampled population has a mean 48 and standard deviation 18, then the mean and the standard deviation for the sampling distribution of (X-bar) for n = 9 are: A. 48 and 18 B. 48 and 9 C. 16 and 6 D. 48 and 6 E. 48 and 2 2. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be more than 94 lbs. is: A. 34.13% B. 84.13% C. 15.87% D. 56.36% E. 16.87%
3. If a population distribution is known to be normal, then it follows that: A. The sample mean must equal the population mean B. The sample mean must equal the population mean for large samples C. The sample standard deviation must equal the population standard deviation D. All of the above E. None of the above
4. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is more than 3.16 inches? A. 5.48% B. 97.72% C. 94.52% D. 44.52% E. 2.28%
5. Whenever the population has a normal distribution, the sampling distribution of is normal or near normal distribution: A. For only large sample sizes B. For only small sample sizes C. For any sample size D. For only samples of size 30 or more
Chapter 9 6. The width of a confidence interval will be: A. Narrower for 99% confidence than 95% confidence B. Narrower for a sample size of 100 than for a sample size of 200 C. Wider for 95% confidence than 90% confidence D. Wider when the sample standard deviation (s) is small than when s is large 7. As standard deviation increases, samples size _____________ to achieve a specified level of confidence. A. Increases B. Decreases C. Remains the same 8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 150. A. Wider than B. Narrower than C. Equal to 9. When a confidence interval for a population proportion is constructed for a sample size n =30 and the value of p =.4, the interval is based on: A. The Z distribution without continuity correction B. The Z distribution with continuity correction C. Skewed distribution D. None of the above
10. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a variance of .09. What is the 90% confidence interval for the true mean length of the bolt? A. 2.8355 to 3.1645 B. 2.5065 to 3.4935 C. 2.8140 to 3.1860 D. 2.4420 to 3.5580 E. 2.9442 to 3.0558 11. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company? A. .1608 to .2392 B. .1992 to .2008 C. .1671 to .2329 D. .1485 to .2515 E. .1714 to .2286 12. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing). The historical records show that over the past 8 years 70 percent of the accounts have been current. Determine the sample size needed in order to be 95% confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company. A. 1842 B. 1548 C. 897 D. 632 E. 1267
Chapter 10 13. When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the ___________ distribution. A. t B. Z C. Binomial D. Skewed distribution 14. For a given hypothesis test if we do not reject H0 and H0 is true. A. No error has been committed B. Type I error has been committed C. Type II error has been committed D. Type III error has been committed 15. If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .10 A. Always B. Sometimes C. Never
16. If a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation and the same mean) will _________ be rejected at the same significance level. A. Always B. Sometimes C. Never
17. A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average more than 22 points per game. Which of the following are the appropriate hypotheses for this problem? A. H0: 21 vs. H: > 21 B. H0: 22 vs. H: > 22 C. H0: 21 vs. H: < 21 D. H0: 22 vs. H: < 22
18. When carrying out a large sample test of H0: = 10 vs. Ha: > 10 by using a critical value, we reject H0 at level of significance when the calculated test statistic is: A. Less than z B. Less than- z C. Greater than z/2 D. Greater than z E. Less than the p value Chapter 13 19. In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) _____ have the same sign. A. Always B. Sometimes C. Never D. Cannot say
20. The least squares regression line minimizes the sum of the A. Differences between actual and predicted Y values B. Absolute deviations between actual and predicted Y values C. Absolute deviations between actual and predicted X values D. Squared differences between actual and predicted Y values E. Squared differences between actual and predicted X values 21. The ___________ the R2 and the __________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable. A. Higher, lower B. Lower, higher C. Lower, lower D. Higher, higher 22. In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the A. Coefficient of determination B. Slope of the regression line C. Y intercept of the regression line D. Correlation coefficient E. Standard error 23. A simple bivariate regression analysis with 21 observations would yield ________ degrees of freedom error and _________ degrees of freedom total. A. 1, 20 B. 18, 19 C. 19, 20 D. 1, 19 E. 18, 20 24. The correlation coefficient may assume any value between A. 0 and 1 B. – and C. 0 and 8 D. -1 and 0 E. -1 and 1 25. In simple regression analysis, if the correlation coefficient is a positive value, then A. The Y intercept must also be a positive value B. The coefficient of determination can be either positive or negative, depending on the value of the slope C. The slope of the regression line must also be positive D. The least squares regression equation could either have a positive or a negative slope E. The standard error of estimate can either have a positive or a negative value
Essay type Questions (2 points each) (Must show your work to receive full points) Chapter 8 1 Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight less than 15.97 ounces?
Chapter 9 2. A sample of 25 items yields = 60 grams and s = 9 grams. Assuming a normal parent distribution, construct a 99 percent confidence interval for the population mean weight.
3. Of a random sample of 600 trucks at a bridge, 150 had bad signal lights. Construct a 95 percent confidence interval for the percentage of trucks that had bad signal lights. 4. A cable TV company wants to estimate the percentage of cable boxes in use during an evening hour. An approximation based on previous surveys is 30 percent. The company wants the new estimate to be at the 90 percent confidence level and within 2 percent of the actual proportion. What sample size is needed?
5. Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 3 percentage points of the actual proportion.
Chapter 10 (show the critical or table values and the calculated values for test statistics in all hypothesis test questions)
6. Test H0: 8 versus HA: > 8, at = 0.05 and 0.01, given n = 25, = 8.07 and s = 0.16. Assume the sample is selected from a normally distributed population.
7. Test H0: π = 0.25 versus HA: π 0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.
8. Test at α =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system?
9. Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded a mean of 2.76 years and s = 0.8. Use = 0.01. Assume normal distribution.
Chapter 13 10. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):
|Brand||Price (X)||Score (Y)|
Use the above data to develop and estimated regression equation and interpret the coefficients. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3200. Finally, test the significance of the slope coefficient. (Note that you need to provide necessary interpretations to get full points).