Consider a random sample of size n = 31, with sample mean \bar{x}=45.2 and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence int

boitshupoO 2021-05-05 Answered

Consider a random sample of size n = 31, with sample mean 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.

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Expert Answer

2abehn
Answered 2021-05-06 Author has 88 answers
Given
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%:tα2=1.697
95%:tα2=2.042
99%:tα2=2.750
The confidence interval is:
xtα2{˙sn  x+tα2sn˙
Fill in the known values: NSL 45.2tα2{˙5.331  45.2+tα2{˙5.331
Simplify:
90%:43.5846 to 46.8154
95%:43.2562 to 47.1438
99%:42.5823 to 47.8177
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