Question

According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours different from the recommended number of hours per unit? The data show the results of a survey of 11 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population. 1.5, 2.2, 3.4, 3.1, 4.1, 0.8, 1.3, 3.9, 4.1, 3.9, 1.5 What can be concluded at the a = 0.01 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: HO: H: o 9 c. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.)

Answer 1

Solution

Part (a)

Test

One-sample t-test for population mean. Answer 1

Part (b)

Hypotheses:

Null H₀: µ = µ₀ = 2   Vs    Alternative H_A: µ ≠ 2 Answer 2

Part (c)

Test statistic:

t = (√n)(Xbar - µ₀)/s = 1.851 Answer 3

where

n = sample size;

Xbar = sample average;

s = sample standard deviation.

Details of calculations

n	11
µ0	2.0
Xbar	2.7091
s	1.2708
tcal	1.8506
α	0.01
p-value	0.0470

Part (d)

p-value = 0.0470 Answer 4

Conclusion

Since p-value > α, the nullhypothesis is accepted and hence we conclude that the

Statistics students’ study hours is not different from the recommended number of hours. Answer 5

DONE