Respuesta :
Answer:
The value of the test statistic is t=1.12.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the mean amount of time required to reach a customer service representative significantly differs between the two hotels.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The sample 1, of size n1=20 has a mean of 2.65 and a standard deviation of √2.952=1.72.
The sample 2, of size n2=20 has a mean of 2.01 and a standard deviation of √2.952=1.89.
The difference between sample means is Md=0.64.
[tex]M_d=M_1-M_2=2.65-2.01=0.64[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1.72^2+1.89^2}{20}}\\\\\\s_{M_d}=\sqrt{\dfrac{6.531}{20}}=\sqrt{0.327}=0.571[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.64-0}{0.571}=\dfrac{0.64}{0.571}=1.12[/tex]
The test statistics (t-statistic) value will be:
"1.12".
Mean and Standard deviation
According to the question,
The null and alternative hypothesis will be:
[tex]H_0[/tex] : μ₁ - μ₂ = 0
[tex]H_a[/tex] : μ₁ - μ₂ [tex]\neq[/tex] 0
Mean = 2.65 and 1.01
Observations = n₁ = n₂ = 20
Now,
The difference between sample mean.
→ [tex]M_d[/tex] = M₁ - M₂
= 2.65 - 2.01
= 0.64
The estimated standard error will be:
→ [tex]s_M_d[/tex] = [tex]\sqrt{\frac{\sigma_1^2 + \sigma_2^2}{n} }[/tex]
By substituting the values,
= [tex]\sqrt{\frac{(1.72)^2 + (1.89)^2}{20} }[/tex]
= [tex]\sqrt{\frac{6.531}{20} }[/tex]
= [tex]\sqrt{0.327}[/tex]
= 0.571
hence,
The test statistic (t) be:
= [tex]\frac{M_d(\mu_1 -\mu_2)}{s_M_d}[/tex]
= [tex]\frac{0.64-0}{0.571}[/tex]
= [tex]\frac{0.64-0}{0.571}[/tex]
= 1.12
Thus the above approach is right.
Find out more information about mean here:
https://brainly.com/question/4583894
