Step by step solution to "Consider a random sample of size n =..."

boitshupoO

Answered question

2021-05-05

Consider a random sample of size n = 31, with sample mean $\overset{―}{x} = 45.2$ and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence intervals for \muμ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

Answer & Explanation

2abehn

Skilled2021-05-06Added 88 answers

Given

\overset{―}{x} = 45.2

n=31

σ = 5.3

Determine the t-value by looking in the row starting with degrees of freedom df=n-1=31-1=30 and in the column with c=90%/95%/99% in table 4:

90 % : t_{\frac{α}{2}} = 1.697

95 % : t_{\frac{α}{2}} = 2.042

99 % : t_{\frac{α}{2}} = 2.750

The confidence interval is:

\overset{―}{x} - t_{\frac{α}{2}} \dot{{} \frac{s}{\sqrt{n}} \to \overset{―}{x} + t_{\frac{α}{2}} \dot{\frac{s}{\sqrt{n}}}

Fill in the known values: NSL

45.2 - t_{\frac{α}{2}} \dot{{} \frac{5.3}{\sqrt{31}} \to 45.2 + t_{\frac{α}{2}} \dot{{} \frac{5.3}{\sqrt{31}}

Simplify:
90%:43.5846 to 46.8154
95%:43.2562 to 47.1438
99%:42.5823 to 47.8177

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Didn't find what you were looking for?