Question

The researcher from problem 1 has a graduate student who is exploring doing his master's degree in the area of community-based mental health services. The student wants to assess whether the public health agencies in the southern part of the state have fewer resources than the agencies in the northern part of the state. He obtained survey data from a convenience sample of 12 agencies, 6 from the northern region and 6 from the southern region. The survey items used this response scale about their funding: 3 = more than enough funding, 2 = about enough funding, 1 = not enough funding (the survey did not interval level data). Here are the data:

Northern: 3, 3, 2, 1, 3, 2

Southern: 2, 1, 3, 2, 1, 2

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_Northern< u_Southern
Alternative hypothesis: u_Northern > u_Southern

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.4534
DF = 10

t = [ (x₁ - x₂) - d ] / SE

t = 1.103

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 1.103.

Therefore, the P-value in this analysis is 0.148.

Interpret results. Since the P-value (0.148) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the public health agencies in the southern part of the state have fewer resources than the agencies in the northern part of the state.