Question

Jim has to select one of the two call centers to handle customer service for his business. The call center B charges more than the call center A with the claim that their (B’s) rating for call satisfaction is very high. Jim obtains the contacts of randomly selected callers for the two companies and ask the level of satisfaction on a 0-10 scale to test the hypotheses (symbols have their usual meaning) The data are below Satisfaction ratings A 6.6 6.6 7.1 4.8 4.8 9.0 7.6 8.3 6.3 5.6 6.9 Satisfaction ratings B 8.8 8.3 8.5 8.1 8.0 8.7 8.0 8.8 7.9 8.6 8.0 8.6 Consider the side by side box plots given below a) do you see any strong outliers? b) test the above hypotheses at 1% level of significance, write the test statistic, and the P_value.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_A> u_B
Alternative hypothesis: u_A < u_B

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.4162
DF = 21

t = [ (x₁ - x₂) - d ] / SE

t = -4.25

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of -4.25.

Therefore, the P-value in this analysis is less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that call center B charges more than the call center A with the claim that their (B’s) rating for call satisfaction is very high.