Learning Goal: I’m working on a data analytics exercise and need an explanation and answer to help me learn.Section I: 36 points total (3 points each problem) Circle the correct answer for the multiple-choice questions below. 1) The Central Limit Theorem is important in statistics because 2) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary? 3) A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence? 4) An economist is interest in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should NOT be more than $100? 5) A _____________________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis. 6) A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you were conduct a test to determine whether the auditor should conclude that there is evidence that the mean balance is difference from $75, which test would you use? A) Z-test of a population mean B) Z-test of a population proportion C) t-test of population mean D) t-test of a population proportion 7) The t-test for the mean difference between 2 related populations assumes that the The population sizes are equal.

The sample variances are equal.

The population of differences is approximately normal or sample sizes are large enough.

All of the above.

8) In testing for differences between the means of two related populations, the null hypothesis is A) : μD = 2 B) : μD = 0 C) : μD < 0 D) : μD > 0 9) A test for whether one proportion is greater than the other can be performed using the chi-square distribution. A) True B) False 10) A test for the difference between two proportions can be performed using the chi-square distribution. A) True B) False 11) The slope (b1) represents A) The predicted value of Y when X = 0. B) The estimated average change in Y per unit change in X. C) The predicted value of Y. D) The variation around the sample regression line. 12) The Y-intercept (b0) represents A) The predicted value of Y when X = 0. B) The estimated average change in Y per unit change in X. C) The predicted value of Y. D) The variation around the sample regression line. Section II: 36 points total Please show your works step by step Problem 1: Find a symmetrically distributed interval around µ that will include 90% of the sample means when µ = 286, σ = 12, and n = 9. (5 points) Problem 2: A random sample of n = 49 has = 72 and S = 7. Form a 99% confidence interval for μ. (5 points) Problem 3: Please use a two tail t-test to solve this problem given the following conditions: n = 9, α = .05, µ = 270, = 276 and S = 12. (5 points) Problem 4: Please use the paired difference test to solve this problem given the following conditions. (5 points) Employee # Before (1) After (2) Difference (Di) 1 8 11 2 7 5 3 11 19 4 9 17 5 6 6 6 8 14 7 10 20 8 8 18 9 11 13 10 9 10 If α = .05, should we reject or accept H0? (2 points) Problem 5: Using the following regression analysis output to answer problems 5A – 5G. (Circle the correct answer.) (2 points each, 14 total) Correction (Summer 2020). X is Time (in Years) NOT Price. Y is Sales in Thousands of Dollars. 5A) The regression equation is: = -48.1928 + 161.3855x

= 161.3855 – 48.1928x

= 161.3855 + 12.654x

= 26.1607 – 6.1690x

= 26.1607 – 6.1690x

5B) This model predicts that the estimated sales in 3 years is: $16,807

$49,912

$41,703

$40,169

$59,021

5C) Which one of the statement A-E is the correct interpretation of R square? 88.7% of sales increased of candy bar were correctly predicted by the model.

78.39% of candy bar sales are explained by the year.

We can expect the model to correctly predict about 16.29% of the sales.

The regression line either passes through or is very close to 98.7% of the points in the scatter plot.

None of the above statements are correct.

5D) Which one of the statement A-E is the correct interpretation of the slope of the regression line? The model predicts an increase in candy bar sales of $48,192.80, on average, each additional year.

The model predicts a decrease in candy bar sales of $48,192.80 on average, each additional year.

The model predicts an increase of candy bar sales of $161,386 on average, each additional year.

The model predicts a decrease in candy bar sales of $3,810 on average, each additional year.

None of the above statements are correct.

5E) Which is the correct interpretation of the Y-intercept? There is no practical interpretation since one cannot have zero years of sales.

The model predicts that the annual sale is $161.39 at year zero.

The model predicts a sales increase of $161.39 annually.

The model predicts a sales increase of $11369.40 annually.

None of the above statements are correct.

5F) Which is the correct interpretation of the Standard Error of the Estimate? $16,300 is the standard deviation of year.

78.2% of the variation in the sales is explained by the variation in years.

For each additional year, the prediction error increases by approximately $16,300.

$16,300 is the standard deviation of the observed annual sales around the regression line.

None of the above statements are correct.

5G) At alpha (α) =.05, can we reject the null hypothesis that the slope of the population regression line is zero? No, because alpha (α) is equal to p-value.

Yes, because a sample size of 6 is big enough to determine that the normality assumption has been met.

Yes, because the slope of the least square line is -48.1928, and not zero.

Yes, because p-value 0.0189 < .05 (α).

Can’t be determined from the information given

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