Question

At α=0.01, test the claim that there is no significant difference between the average salaries of registered nurses and physician assistants in Ontario. Random samples of 39 registered nurses and 56 physician assistants have been selected across the province. The following table contains means for both samples. We also assume that the variability of these numbers didn't change since the last time the study was conducted and the population standard deviations are still available. Assume that the z-distribution can be used for hypothesis testing. Employees Sample Mean x̄ Population Std. Dev. σ Sample Size Registered Nurses 69,792 6,670 39 Physician Assistants 72,883 10,846 56 Hint: Use the test statistic formula: z=(x̄1−x̄2)−(μ1−μ2)/√(σ1²/n1+σ2²/n2) (a) State the null and alternative hypotheses, and identify which one is the claim. H0: μ₁ - μ₂ = 0 H1: μ₁ - μ₂ ≠ 0 Which one is the claim: H0 For parts (b), (c) use the POSITIVE sign for the z-value and test statistic, and round your answers to 3 decimal places. (b) What is the critical z-value? (c) What is the test statistic? (d) Is the null hypothesis rejected? Yes No (e) Is the claim supported? At 1% significance level, there is sufficient evidence to warrant rejection of the original claim. It can not be concluded that there is a difference between the average salaries of nurses and physician assistants. At 1% significance level, there is not sufficient evidence to warrant rejection of the original claim. There is a difference between the average salaries of nurses and physician assistants. At 1% significance level, there is not sufficient evidence to warrant rejection of the original claim. It can not be concluded that there is a significant difference between the average salaries of nurses and physician assistants. At 1% significance level, there is sufficient evidence to warrant rejection of the original claim. It can be concluded that there is a significant difference between the average salaries of nurses and physician assistants. None of the above.

          At α=0.01, test the claim that there is no
significant difference between the average salaries of registered
nurses and physician assistants in Ontario. Random samples of 39
registered nurses and 56 physician assistants have been selected
across the province. The following table contains means for both
samples. We also assume that the variability of these numbers
didn't change since the last time the study was conducted and the
population standard deviations are still available. Assume that
the z-distribution can be used for hypothesis
testing.  
Employees
Sample Mean x̄
Population Std. Dev. σ
Sample Size
Registered Nurses
69,792
6,670
39
Physician Assistants
72,883
10,846
56
Hint: Use the test statistic
formula: z=(x̄1−x̄2)−(μ1−μ2)/√(σ1²/n1+σ2²/n2)
(a)
State the null and alternative hypotheses, and identify which one
is the claim. 
H0: μ₁ - μ₂ = 0
H1: μ₁ - μ₂ ≠ 0
Which one is the claim: 
H0
For parts (b), (c) use the POSITIVE sign for
the z-value and test statistic, and round your answers to 3
decimal places.
(b) What is the critical z-value? 
(c) What is the test statistic? 
(d) Is the null hypothesis rejected? 
Yes
No
(e) Is the claim supported? 
At 1% significance level, there is sufficient evidence to
warrant rejection of the original claim. It can not be concluded
that there is a difference between the average salaries of nurses
and physician assistants.
At 1% significance level, there is not sufficient evidence to
warrant rejection of the original claim. There is a difference
between the average salaries of nurses and physician
assistants.
At 1% significance level, there is not sufficient evidence to
warrant rejection of the original claim. It can not be concluded
that there is a significant difference between the average salaries
of nurses and physician assistants.
At 1% significance level, there is sufficient evidence to
warrant rejection of the original claim. It can be concluded that
there is a significant difference between the average salaries of
nurses and physician assistants.
None of the above.

Added by Consuelo J.

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