Question

A problem with a phone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telecommunications company. The file Phone contains samples of 20 problems reported to two different offices of a telecommunications company and the time to clear these problems (in minutes) from the customers’ lines:

Central Office I Time to Clear Problems (minutes)

1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10

1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97

Central Office II Time to Clear Problems (minutes)

7.55 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02

3.75 0.65 1.92 0.60 1.53 4.23 0.08 1.48 1.65 0.72

Perform a hypothesis test to determine if there’s evidence in this data of a difference in the mean waiting time between the two offices by answering the following questions:

(a) What are the null and alternate hypotheses for this test?

(b) Assuming that the population variances from both offices are equal, what is the value of the test statistic?

(c) Using the critical value approach, is there evidence of a difference in the mean waiting time between the two offices? (Use α = 0.05.) (Answer this using complete sentences and be sure to include what decision rule you used to arrive at your conclusion.)

(d) Find the p-value in (c) and interpret its meaning.

(e) What assumption (other than equal variances) is necessary in (c)?

(f) Assuming that the population variances from both offices are equal, construct and interpret a 95% confidence interval estimate of the difference between the population means in the two offices.

Answer 1

9 Rejection region : for 2=0.05 te=2.024, d. f = 38 R= pt: 1772.0243 since Itl = 0.354 <2.024 so we fail to reject the null hypothesis. ge there is sufficient evidence to conclude that there is no significant difference blo two means. d) P-value = 0.725 Since P-value is greater than &=0:05. so we accept the null hypothesis. e) Assumption for t-test u The population are normally distributed The Samps Population Standarel dewication are unknown - (ii) the observation are independent. f) 95% confidence Internal i te = 2:024, d=0,05 at dif 238 n lemn

som let for central office I Time to clear . problems (minutes) Xi = 2.214, si = 10718 , Diado for central office I time to clear problems (minutes) X = 210115, B2 = 1.8917, ng=20 claim The data mean is significant difference. a) null and alternative hypothesis: Ho: li-la Hii le Ela I b Assume the population variance are equal. Test Statistics t= x - Xe (91-1937? +(12-138? tbl N nitra-2 = 2.214- Q.0115 119 x (1171892 +19x61189173211 +11 V + 20+20-2 1.20 20 = 0.354 P-value = 0.725

Pooled standard deviation sp = J Chin) 8,² + 122-1) 22 V metna-2 s ” (20-1) x[1.718.72 +620-13 (Iroq 1912 20+20-2 =1:807 Standard error, SiE = So II += = 1.807 ott m2 20 20 50.571 CI = (+2) + te XS.E (2:214-2.012) † 2.024*0571 = (-0.954111359)