Question

Students and faculty alike are concerned about the cost of textbooks. A committee of both students and faculty searched the internet for appropriate books that would be available for less than $60. A random sample of 40 texts gave a mean of $65.12 with a standard deviation of $23.08. At the 5% level of significance, do the texts selected in the sample cost significantly more than the amount the committee considered appropriate?

(1) List all the information necessary for conducting the hypothesis test and state which

test you are doing.

(2) State the null and alternative hypotheses and whether you would use a right-tailed

test, a left-tailed test, or a two-tailed test.

(3) Sketch the critical reason, indicating on the sketch what the critical value(s) are.

(4) Determine the calculated z or t.

(6) Decide if you will Reject or Fail to Reject the Null Hypothesis.

(7) Interpret your conclusion in terms of the problem.

(8) If there are any questions to be answered in the problem, do so.

Answer 1

Claim: The cost significantly more than the amount the committee considered appropriate that is $60

(1) List of information

n = sample size = 40 texts

s = sample standard deviation = 23.08

One-sample t-test is used here since the population standard deviation is unknown.

(2) The null and alternative hypothesis

Claim:

The alternative hypothesis contains more than sign, so the test is a right-tailed test.

(3) Critical value and region

alpha = significance level = 5% = 0.05

degrees of freedom = n - 1 = 40 - 1 = 39

Using t distribution table the critical value with area 0.05 in one-tailed and degrees of freedom 39 is 1.685

For a right-tailed test there is only one critical value and which is positive.

Critical value = 1.685

(4) Calculated t

The formula of t-test statistics,

(5) Decision rule:

If test statistics fall in the critical region then reject the null hypothesis otherwise fail to reject the null hypothesis.

Test statistics 1.403 does not fall in the critical region so it fail to reject the null hypothesis.

(6) Conclusion

Fail to reject the null hypothesis, that is there is not sufficient evidence to support the claim that the more than the amount the committee considered appropriate that is $60.

(7) No need for any questions to be answered, all were answered.