Give and interpret the 95% confidence intervals for males and a second 95% confidence interval for...

Give and interpret the 95% confidence intervals for males and a second 95% confidence interval for females on the SLEEP variable. Which is wider and why?

Known values for Male and Female:

Males: Sample Size = 17; Sample Mean = 7.765; Standard Deviation = 1.855

Females: Sample Size = 18; Sample Mean = 7.667; Standard Deviation = 1.879

Using t-distribution considering sample sizes (Male/Female count) are less than 30

Expert Solution

1) For males
n = 17  Sample Size
X̅ = 7.765  Sample Mean
s = 1.855  Sample Standard Deviation
For 95% confidence interval,
α = 1 - 0.95 = 0.05

Finding 95% confidence interval of the mean using t Distribution
Confidence interval for mean is given using Excel function CONFIDENCE.T

is given by Excel function CONFIDENCE.T

X̅ ± CONFIDENCE.T(α, s, n)
= 7.765 ± CONFIDENCE.T(0.05, 1.855, 17)
= 7.765 ± 0.9538
= (6.8112, 8.7188)
95% confidence interval of the mean percentage using t Distribution = (6.8112, 8.7188)

2) For females
n = 18  Sample Size
X̅ = 7.667  Sample Mean
s = 1.879  Sample Standard Deviation
For 95% confidence interval,
α = 1 - 0.95 = 0.05

Finding 95% confidence interval of the mean using t Distribution
Confidence interval for mean is given using Excel function CONFIDENCE.T
  is given by Excel function CONFIDENCE.T

X̅ ± CONFIDENCE.T(α, s, n)
= 7.667 ± CONFIDENCE.T(0.05, 1.879, 18)
= 7.667 ± 0.9344
= (6.7326, 8.6014)
95% confidence interval of the mean percentage using t Distribution = (6.7326, 8.6014)

Of the two confidence intervals, the one for the males have a greater difference between the lower and upper bounds
Hence, the confidence interval for the males is wider.
This is because, the sample size for males is lower, hence, the Margin of Error given by         is high

milcah answered 3 months ago

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