Question

“Have you changed industries in the last 12 months?” This question was asked in a LinkedIn survey in 2016 of two independent random samples representing two populations: Population 1: all Millennial workers that are currently employed Population 2: all non-Millennial workers that are currently employed The researcher would like to assess if the proportion of all Millennial workers who are currently employed and have changed industries in the last 12 months would be less than the proportion of all non-Millennial workers who are currently employed and have changed industries in the last 12 months. The significance level is set to 5%. The results of the study are summarized below. Sample Size Number who have changed industries in the last 12 months Sample proportion 1 = Millennial workers 72 40 0.5556 2 = Non-Millennial workers 48 31 0.6458 (Challenge: Before looking at the questions, use the information provided in this background and work through the 4 steps of testing theories yourself, and then use your results to answer these questions ~ good practice.) Question 7 Subquestions 7.a 0.5 point(s) The researcher sets up the null hypothesis as H0: p1 = p2. Select the appropriate alternative hypothesis. Ha: p1 ≠ p2 Ha: p1 > p2 Ha: p1 < p2 7.b 0.5 point(s) It is important to understand what the various symbols representing computational quantities mean. Consider the following incorrect definition for the parameter p2. “p2 is the sample proportion of non-Millennial workers who have changed industries in the past 12 months.” Provide the two words to complete this statement: This would be the correct definition of the parameter p2 if you replace the word _____________ with the word _______________. replace the word p2 with the word p̂2 . replace the word non-Millennial with the word Millennial . replace the word sample with the word population . replace the word proportion with the word amount . 7.c 0.5 point(s) Which of the following is the best estimate of that common population proportion p? 0.6097 0.5917 0.4083 0.3520 7.d 0.5 point(s) It seems that the sample sizes of 72 and 48 should be sufficiently large enough to use a normal approximation to compute the p-value. (i) State the condition that is needed. (ii) Provide verification that the sample sizes are large enough. Be sure to include the appropriate notation. (i) "State": n1p1 ≥ 10, n1(1-p1) ≥ 10, n2p2 ≥ 10, n2(1-p2) ≥ 10. (ii) "Check": n1(p̂1) = 72(0.5556) = 40 ≥ 10, n1(1-p̂1) = 72(1 - 0.5556) = 32 ≥ 10, n2(p̂2) = 48(0.6458) = 31 ≥ 10, n2(1-p̂2) = 48(1 - 0.6458) = 17 ≥ 10. (i) "State": n1p̂1 ≥ 10, n1(1-p̂1) ≥ 10, n2p̂2 ≥ 10, n2(1-p̂2) ≥ 10. (ii) "Check": n1(p̂1) = 72(0.5556) = 40 ≥ 10, n1(1-p̂1) = 72(1 - 0.5556) = 32 ≥ 10, n2(p̂2) = 48(0.6458) = 31 ≥ 10, n2(1-p̂2) = 48(1 - 0.6458) = 17 ≥ 10. (i) "State": n1p1 ≥ 10, n1(1-p1) ≥ 10, n2p2 ≥ 10, n2(1-p2) ≥ 10. (ii) "Check": n1(p̂) = 72(0.5917) = 42.6024 ≥ 10, n1(1-p̂) = 72(0.4083) = 29.3976 ≥ 10, n2(p̂) = 48(0.5917) = 28.4016 ≥ 10, n2(1-p̂) = 48(0.4083) = 19.5984 ≥ 10. (i) "State": n1p̂ ≥ 10, n1(1-p̂) ≥ 10, n2p̂ ≥ 10, n2(1-p̂) ≥ 10. (ii) "Check": n1(p̂) = 72(0.5917) = 42.6024 ≥ 10, n1(1-p̂) = 72(0.4083) = 29.3976 ≥ 10, n2(p̂) = 48(0.5917) = 28.4016 ≥ 10, n2(1-p̂) = 48(0.4083) = 19.5984 ≥ 10. 7.e 0.5 point(s) Using the results of the study, complete the following statement: The sample proportion of Millennial workers who are currently employed and have changed industries in the last 12 months (p with hat on top subscript 1) is ____________ (null) standard errors __________ the sample proportion of non-Millennial workers who are currently employed and have changed industries in the last 12 months (p with hat on top subscript 2). -0.9848, below -0.9848, above 0.9848, below 0.9848, above 7.f 0.5 point(s) The p-value is 0.1624, at a 5% significance level, the statistical decision is to fail to reject H0, the results are not statistically significant. What can be said about the p-value 0.1624. Select all the statements that apply. The probability that the proportion of all Millennial workers who are currently employed and have changed industries in the last 12 months equals the proportion of all non-Millennial workers who are currently employed and have changed industries in the last 12 months is 0.1624. If the two population proportions are equal, that is assuming the proportion of all Millennial workers who are currently employed and have changed industries in the last 12 months equals the proportion of all non-Millennial workers who are currently employed and have changed industries in the last 12 months, the probability of observing a test statistic value like the one we got or something smaller is 0.1624. The probability of observing a test statistic value like the one we got or something smaller is 0.1624. If we were to repeat this study many times and if the two population proportions are equal, that is assuming the proportion of all Millennial workers who are currently employed and have changed industries in the last 12 months equals the proportion of all non-Millennial workers who are currently employed and have changed industries in the last 12 months, we would expect to observe a test statistic value like the one we got or something smaller in 16.24% of the repetitions. 7.g 0.5 point(s) Suppose the two population proportions are equal, that is assume the proportion of all Millennial workers who are currently employed and have changed industries in the last 12 months equals the proportion of all non-Millennial workers who are currently employed and have changed industries in the last 12 months. If we were to repeat this study 80 times, each time taking independent random samples of the same size, conducting the same hypothesis test at the same signficance level (previously stated to be 5%), then how many decisions would we expect to be incorrect? 5% 40 4 None Can't be determined.

Answer 1

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