Answer to Question #106788 in Statistics and Probability for Yusuf

Question

Mmabatho the Social Scientist took a random sample of 30 adults with Autism Spectrum Disorder (ASD) and found their reading time to be normally distributed with sample mean and sample
standard deviation of 90 wpm and 18 wpm respectively.

Question 6
What is the upper limit for the 95% confidence interval estimate of the population mean?
(1) 96:7206:
(2) 96:4412:
(3) 83:5588:
(4) 83:2794:
(5) None of the above

Answer 1

Since the population standard deviation is unknown, the sample mean follows a t(n-1) distribution with mean $\mu$ and standard deviation$\frac{s}{\sqrt{n}}$

From t-table or =T.INV(0.975,29) Excel formula, $t(29, 0.05)=2.04523$

Upper 95% CI is given by $90+(2.04523×\frac{18}{\sqrt{30}})=90+6.72131=96.72131$

Similarly, the answer can be obtained from =90+CONFIDENCE.T(0.05,18,30) Excel formula. Thus, the correct answer is (1)