Mathematics: Below is the output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. What is the smallest level of significance at which the null hypothesis will still not be rejected? Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386

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Below is the output from a study to see whether

lyssssasantiago9844

13.06.2021

Solution :

a). $\text{Set up hypothesis}$

$\text{Null hypothesis}$ : There is no significance between them.

$H_0:\mu_1=\mu_2$

$\text{Alternate hypothesis}$ : There is significance between them.

$H_1:\mu_1!=\mu_2$

b). Test statics

$X(\text{mean}) = 2.214$

Standard deviation $(s.d1)=1.718; \text{Number}(n_1)=20$

$Y(\text{mean})=2.0115$

Standard deviation $(s.d2)=1.8917; \text{Number}(n_2)=20$

We use the test statics :

$t=\frac{X-Y}{\sqrt{\frac{s.d1^2}{n_1}+\frac{s.d2^2}{n_2}}}$

$t_0=\frac{2.214-2.0115}{\sqrt{\frac{2.95152}{20}+\frac{3.57853}{20}}}$

$t_0=0.35$

$|t_0|=0.35$

c. The critical value of |t| with minimum $(n_1-1)$ , i.e. 19 d.f is $2.093$

We got $|t_0|$ = 0.35439 and |t| = 2.093

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