An article indicates that self-esteem was an important predictor of those who will benefit from treatment for bulimia. The table gives the mean and standard deviation of self-esteem scores prior to treatment, at posttreatment, and during a follow-up.

PretreatmentPosttreatmentFollow-upSample Meanx20.426.827.8Standard Deviations5.17.68.3Sample Sizen252524

(a)

Use a test of hypothesis to determine whether there is sufficient evidence to conclude that the true pretreatment mean is less than24. (Use= 0.05.)

State the null and alternative hypotheses.

H₀:= 24 versusH_a:24

H₀:< 24 versusH_a:> 24

H₀:< 24 versusH_a:= 24

H₀:= 24 versusH_a:< 24

H₀:24 versusH_a:= 24

State the test statistic. (Round your answer to three decimal places.)

t=

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t>t<

State the conclusion.

H₀is not rejected. There is sufficient evidence to conclude that the pretreatment mean is less than 24.

H₀is rejected. There is insufficient evidence to conclude that the pretreatment mean is less than 24.

H₀is not rejected. There is insufficient evidence to conclude that the pretreatment mean is less than 24.

H₀is rejected. There is sufficient evidence to conclude that the pretreatment mean is less than 24.

(b)

Construct a 95% confidence interval for the true posttreatment mean. (Round your answers to two decimal places.)

to

(c)

Without a formal statistical test, what might you conclude about the differences among the three sampled population means represented by the results in the table?

The pretreatment mean looks considerably smaller than the posttreatment mean only.

The pretreatment mean looks the same as the other two means.

The pretreatment mean looks considerably smaller than the other two means.

The pretreatment mean looks considerably larger than the posttreatment mean only.

The pretreatment mean looks considerably larger than the other two means.

You may need to use the appropriateappendix tableto answer this question.