One of your first tasks as an intern in the NCSU Financial Aid Office is to esti

Question

One of your first tasks as an intern in the NCSU Financial Aid Office is to estimate the mean cost of textbooks for the current semester incurred by full-time students majoring in the biological sciences. From a random sample of 10 full-time students majoring in biological science you obtain the following textbook costs for the current semester (in dollars):

500, 650, 600, 505, 450, 550, 515, 495, 650, 395

Question 1. Find a 95% confidence interval for the mean cost of textbooks for the current semester incurred by full-time students majoring in the biological sciences (do not include dollar signs in your answer):

lower bound?

upper bound?

Do these data give good reason to believe that the mean cost of textbooks for the current semester incurred by full-time students majoring in the biological sciences is greater than $500? Perform the appropriate hypothesis test and answer the questions below.

Question 2a. What is the value of the test statistic t for this test?

Question 2b. Use this t-table to determine bounds on the P-value of this test:

lower bound on the P-value
upper bound on the P-value

Explanation / Answer

The sample given is 500, 650, 600, 505, 450, 550, 515, 495, 650, 395

Find mean and sd

n =10

mean = 531

std dev = 78.54

df = 9

t value for 95% = 2.2621

Margin of error = 2.2621 * 78.54/(rt9)

= 59.222

Hence confidence interval lower bound = 531- 59.222 = 471.788

Upper bound = 531+59.222 = 570.222

----------------------------------------------

H0: mu =500

Ha: mu > 500

Mean diff = 31

t statistic = 31/std error = 31/26.18

=1.184

p value = .13337.

The result is not significant at p < .05.

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