For an internet provider, it is claimed that the average time it takes a technic

Question

For an internet provider, it is claimed that the average time it takes a technician to install and setup internet at a new location is 30 minutes. The population standard deviation is known to be sigma = 10 minutes. For quality control, each week a randomly selected technician is audited to see if there installation time is running longer than the claimed 30 minutes, on average. Below are 5 randomly selected installation times from an audited technician. Assume the population is normally distributed. Find the p-value for the test of the following hypotheses: H_0: mu = 30 minutes H_a: mu > 30 minutes 0.8273 0.1727 0.2040 0.7960 Provide the 95% confidence interval for the true average time it takes this technician to complete an internet installation at a new location. (26.34 min, 41.06 min) (24.94 min, 42.47 min) (27.28 min, 40.12 min) (17.25 min, 50.15 min)

Explanation / Answer

11)

std error of mean =std deviation/(n)1/2 =10/(5)1/2 =4.472

therefore test stat z=(X-mean)/std error =(33.7-30)/4.472 =0.8273

for above test stat p value =0.2040

12)

for 95% CI; z=1.96

hence 95% interval =sample mean -/+ z*std error =24.94 ; 42.47

X 36.5 44.1 27.6 31.4 28.9 Mean 33.7

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