Question

Aprobion with a phone line that prevents a customer from receiving or making calls uptening to both the customer and the telephone company. Samples of 20 probians raported to two different offices of a phone company and the ima to hear these probiert in minutes from the customernes are provided. Complete (a) through id below. Cik here to view the same times Assuming that the population variances from both offices are equal, la there evidence of a difference in the mean waiting times between the two ofi? (USA=0.05) Lot be the mean wating time of the frototice and be the mean waiting time of the moond office. Determine the hypotheses. Choose the correct answer below. OAH 0 OB H20 H0 OCH 50 OD HOW H10 Determine the test statistic In Pound to four decimal processended) Determine the article The nical value)) (Use a conme to parte anawenas noted. Round to four decimal pos as neded) Choose the correct conclusion below O A Donject Hy. There is sufficient evidence that the mean ditu, O Do not reject. There is ruficient evidence that the means the OC RH. There wfficient widence that the mear difer O Reject. There is insufficient evidence that the means for

Answer 1

This problem is solved by using R

Two sample t test output :

R RGui (32-bit) - [R Console] R File Edit View Misc Packages Windows Help Q@STO > x1=C(1.74,1.76,0.93,2.62,0.57,1.79,4.23,3.86,1.27,3.04,1.02,0.40,0.96,1.89,0.80,1.14,6.18,3.94,5.29,0.80) > x2=C (7.28,3.76,0.10,1.09,0.46,0.37,3.35,2.14,0.45, 4.06,3.90,0.80,1.86,0.64,1.48, 4.04,0.11,1.30,1.63,0.87) > t.test(x1,x2, conf.level=0.95, var.equal=T) TWO Sample t-test data: xl and x2 t = 0.40574, df = 38, p-value = 0.6872 alternative hypothesis: true difference in means is not equal to o 95 percent confidence interval: -0.9055888 1.3595888 sample estimates: mean of x mean of y 2.2115 1.9845 >

Summary :

a. The null and alternative hypothesis will be

$Ho : \mu1 - \mu2 = 0$

$H1 : \mu1 - \mu2 \neq 0$  

Test statistic (t) = 0.4057

Degree of freedom = n1 + n2 - 2 = 38

Critical value = -2.0244 , 2.0244

Conclusion : Do not reject H0 .There is insufficient evidence that the means differ.

b. p- value = 0.6872

c.the following assumptions is necessary for a)

Answer :D. Since the sample sizes are both less than 30, it must be assumed that both sampled populations are approximately normal.

d. 95 % confidence interval for population mean difference is given ( -0.91 , 1.36)

now, interpretation of confidence interval

Answer : C. You can conclude with 95% confidence that the difference between the population mean wait times of the two offices falls inside this interval.

Thank You!