Question

An SRS of 27 students at UH gave an average height of 5.6 feet and a standard deviation of .1 feet.Construct a 90% confidence interval for the mean height of students at UH. a) [5.567, 5.633]b) [5.429, 5.771]c) [5.594, 5.606]d) [4.350, 7.050]e) [4.100, 7.400]f) None of the above

Answer 1

Option a) [5.567, 5.633]

Explanation:

We are given the following in the question:

Sample mean,
`\bar{x}` = 5.6 feet

Sample size, n = 27

Alpha, α = 0.10

Sample standard deviation, s = 0 .1 feet

90% Confidence interval:

`\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 26 and}~\alpha_(0.10) = \pm 1.7056`

`5.6 \pm 1.7056(\displaystyle(0.1)/(√(27)) ) = 5.6 \pm 0.0328 = (5.5672 ,5.6328) \approx (5.567,5.633)`

Option a) [5.567, 5.633]