Question

The BYU testing center is known for being the location with the most prayers said per capita. Researchers asked a random sample of 49 BYU students in winter 2019 to estimate the number of prayers they said in the BYU testing center the previous semester. Researchers plan to use these data to estimate the mean number of prayers said by students the previous semester in the BYU testing center with 99% confidence. They obtained a sample mean of 10.92 prayers with a standard deviation of 7.53. What is the confidence interval estimate?'

Answer 1

Answer: $(8.149,\ 13.691)$

Step-by-step explanation:

Given : Sample size : n= 49, it means its a large sample.

Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Sample mean: $\overline{x}=10.92$

Standard deviation: $\sigma=7.53$

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=10.92\pm (2.576)\dfrac{7.53}{\sqrt{49}}\\\\\approx10.92\pm2.771=(10.92-2.771,10.92+2.771)=(8.149,\ 13.691)$

Hence, the 99% confidence interval for population mean=  $(8.149,\ 13.691)$