Question 2. A researcher hypothesized that people with AIDS would have a lower w

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Question 2. A researcher hypothesized that people with AIDS would have a lower without AIDS. She collected data using a quality of life e score of the 216 AIDS patients was 6.7, with a quality of life than people scale and found that the averag standard deviation of 4.3. She knew that the rest of the population had an average score of 7.1. Do AIDS patients have significantly lower quality of life than the rest of the population? 2. Stating the null hypothesis 3. Selecting the sampling distribution and establishing the critical region 4. Computing the test statistic 5. Making a decision and interpreting the test resuls

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Solution:-

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

Null hypothesis: > 7.1

Alternative hypothesis: < 7.1

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

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

tcritical = - 1.652

We will reject the null hypothesis if t value is less than - 1.652.

SE = s / sqrt(n)

S.E = 0.2926

DF = n - 1 = 216 - 1

D.F = 215

t = (x - ) / SE

t = - 1.37

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.37.

Thus the P-value in this analysis is 0.0853

Interpret results. Since the P-value (0.0853) 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 Aids patients have lower quality of life than the rest of population.

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