Question

A social researcher wants to investigate the level of anxiety that people have based on the individual area of residence (urban vs. rural). The researcher uses alpha level of .05 to determine whether there is a significant difference in the level of anxiety between people who live in rural areas and people who live in urban areas. The data is presented in the table below. Rural Urban 14 13 8 7 n 15 15

a. State the null and alternative hypotheses in symbols.

b. Set up the criteria for making a decision. That is, find the critical value.

c. Compute the appropriate test statistic. Show your work.

d. Based on your answers above, evaluate the null hypothesis.

REJECT FAIL TO REJECT (circle one)

e. State your conclusion in words.

f. Compute the 95% confidence interval.

g. Interpret the confidence interval you calculated above.

Answer 1

a. State the null and alternative hypotheses in symbols.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

b. Set up the criteria for making a decision. That is, find the critical value.

The critical values are -2.048 and 2.048.

c. Compute the appropriate test statistic. Show your work.

t = 1

d. Based on your answers above, evaluate the null hypothesis.

FAIL TO REJECT (circle one)

e. State your conclusion in words.

There is no significant difference in the level of anxiety between people who live in rural areas and people who live in urban areas.

f. Compute the 95% confidence interval.

The 95% confidence interval is -1.048 and 3.048.

g. Interpret the confidence interval you calculated above.

We are 95% confident that the true mean difference in the level of anxiety between people who live in rural areas and people who live in urban areas.

Rural	Urban
14	13	mean
2.828427125	2.645751311	std. dev.
15	15	n
	28	df
	1.000	difference (Rural - Urban)
	7.500	pooled variance
	2.739	pooled std. dev.
	1.000	standard error of difference
	0	hypothesized difference
	1.000	t
	.3259	p-value (two-tailed)
	-1.048	confidence interval 95.% lower
	3.048	confidence interval 95.% upper
	2.048	margin of error