Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t Subscript alpha divided by 2​, ​(b) find the critical value z Subscript alpha divided by 2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 95​%, sigma is not​ known, and the histogram of 57 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

Answer 1

Answer:

The critical value of t is 2.000.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean in case the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

n = 57

Confidence level = 95%

As the sample size is large enough, i.e. n = 57 > 30 the sampling distribution of sample mean can be approximated by the normal distribution.

The distribution of sample statistic is normal and the sample size is quite large. This implies that it is appropriate to use a t-interval.

Compute the critical value of t as follows:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (57-1)}=t_{0.025, 56}=2.000$

*Use a t-table for the critical value.

Thus, the critical value of t is 2.000.

Answer 2

Answer:

The critical value of t is 2.000.

Step-by-step explanation:

Given information:

n=57

The confidence level is 95%

Standard deviation is unknown so we can use normal distribution

Degree of freedom $df=n-1=57-1=56$

$\alpha=1-0.95=0.05$

$\frac{\alpha}{2}=0.025$

T value for $df=56$ and $\frac{\alpha}{2}=0.025$,

By use of t-table critical value.

$t_{0.025,56}=2.000$

Hence the critical value of t is 2.000.

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