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6. The time to repair an electronic instrument is a normally distributed random variable measured in hours. The repair time for 16 such instruments chosen at random are as follows: Hours 159 280 10 212 224 379179 264 222 362 168 250 149 260 485170 (a) You wish to know if the mean repair time exceeds 225 hours. Set up appropriate hypotheses for investigating this issue. (b) Test the hypotheses you formulated in part (a). What are your conclusions? Use a 0.05 (c) Find the P-value for this test.

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Answer #1

Here we need to calculate the mean and SD of data. Following table shows the calculations:

Hours, X (X-mean)A2 159 224 149 280 379 362 260 101 179 168 485 212 264 250 170 3864 6806.25 306.25 380.25 8556.25 1482.25 18906.25 14520.25 342.25 19740.25 3906.25 5402.25 59292.25 870.25 506.25 72.25 5112.25 146202 Total

Sample size: n=16

Mean:

-=-= 241.5

Standard deviation:

Σ (x-x)- = 98.7259 rl

(a-c)

Here we have x=241.5, s-98.7259, n =16 Hypotheses are H 0: μ Ha: μ =225 >225 Level of significance α 0.05 Test is one tailed (right tailed) Degree of freedom: df -n-1-15 Test Statistics: (241.5-225)/(98.7259/sqr s/yM = 0.669 Critical value: Rejection Region: 1.753 If |t| >1.753, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis P-value: P-value-0.2568 Decision: Since p-value is not less than level of significance so we fail to reject the nul hypothesis Excel function for critical value: Excel function for p-value: =TINV(0,1,15) =TDIST(0.669151)

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