Question

In order to compare the satisfaction of customers of 2 competitor companies of , 174 customers of company A and 355 customers of company B were chosen randomly. Customers were required to rate the companies from level 1 (least satisfaction) to 5 (maximum satisfaction). The results are included below. Check whether the difference in the mean level of customers' satisfaction of the two companies is statistical important at 1%. The results are included below:

Company A   Company B
Sample Size   174   355
Sample mean   3.51   3.24
Sample Standard Deviation (S)   0.51   0.52

Answer 1

Given :-

Company A Company B
Sample Size 174 355
Sample mean 3.51 3.24
Sample SD. 0.51 0.52

Level of significant for test : - 0.01 (1%)

Hypothesis to be tested

H0 : mean of company A(X1)=mean of companyB(X2)

H1 : X1 X2

Test to be applied qnd test statistic used

We apply Z test for two population mean beacouse(n) greater than 30,

Test statistic used  

Here we use sample standard deviation

Z = 5.68

Critical Region:

Based on the information provided, the significance level is =0.01, and the critical value for a two-tailed test is =2.58

Zcalculated is is grrater than the z critical value

So that we reject null hypothesis and accept alternative hypothesis.

That is the means of two company is not equal. And the difference of mean is exist.

Confidence Interval

The 99% confidence interval (0.3920.148<μ1​−μ2​<0.392)

Thank you.