A software company has designed a children\'s computer game. Experience indicate

Question

A software company has designed a children's computer game. Experience indicates that the mean time to complete should be 10 minutes or less and the standard deviation should not exceed 3 minutes. The company has decided to test with 10 children selected at random. The following values represent the time (rounded to the nearest minute) each child spent to complete the game. The developers of the software will assume the standard deviation of the time to completion of the game does not exceed 3 minutes unless the data strongly suggest otherwise. State the appropriate null and alternative hypotheses regarding the standard deviation. Use the sample data to conduct the test with a significance level 0.10 12 Choose the correct null and alternative hypotheses below. B. H0.02-10 OC. H0.02 210 OD, Ho.c2 29 s 10

Explanation / Answer

THe correct Null and ALternative Hypothesis

H0 : 2 <= 9

Ha : 2 > 9

Option F is correct.

Test statistic here

X2 = (N-1) (s/ 0)2

Here N = 10; 0 = 3

and for calculating sample standard deviation

s = 3.448 (by calculation of standard deviation)

so X2 = (N-1) (s/ 0)2 = (10 -1) (3.448/3)2 = 11.89

for an upper one tailed test

T > X2 1-0.05, N-1

critical value = 16.9190

so here T < X2critical so we shall not reject the null hypothesis and can conclcude that there is insufficient evidence that 2 > 9. Option F is correcct.

X (x-xbar)^2 8 4 12 4 11 1 12 4 14 16 15 25 16 36 13 9 8 4 Average 12 4 10 Sum 107 Std. Dev. Of sample 3.448

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