Question

Researchers from a payroll services company randomly sampled customer service representatives from two different industries. The...

Researchers from a payroll services company randomly sampled customer service representatives from two different industries. The first sample of 34 customer service representatives worked in banking, and the second sample of 36 customer service representatives worked in telecommunications. The results are given below. Using the 5% significance level, test the claim that the mean hourly wage for these two populations of workers is different (claim: μBμT) by choosing the correct answer choice below.

Sample Size

Mean Salary

Population Standard Deviation
Banking (B)

34

$

14.77

$ 2.55
Telecommunications (T)

36

$

13.82

$

2.32

Which one?

Test statistic: 2.54, Critical values: ±1.96, Conclusion: We support the claim that the mean hourly wage is different.
Test statistic: 1.63, Critical values: ±1.96, Conclusion: We cannot support the claim that the mean hourly wage is different.
Test statistic: 1.63, Critical values: ±1.645, Conclusion: We cannot support the claim that the mean hourly wage is different.
Test statistic: −1.63, Critical values: ±2.326, Conclusion: We do not reject the claim that the mean hourly wage is different.
Test statistic: 2.03, Critical values: ±1.645, Conclusion: We support the claim that the mean hourly wage is different.
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Answer #1

Correct option:

Test statistic: 1.63, Critical values: ±1.96, Conclusion: We cannot support the claim that the mean hourly wage is different.

Explanation:

H0:

HA:

nB = 36

nT = 36

= 0.05

From Table, critical valus of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = 1.63 is less than critical value of Z= 1.96, the difference is not significant. Fail to reject null hypothesis.

Conclusion:We cannot support the claim that the mean hourly wage is different.

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