Question

Based on a random sample of fifty full-time college students, we can be 90% confident that for all college students the mean time spent studying per week is between 9.25 hours and 10.75 hours. Which interval (a – d) is a 95% confidence interval for the same sample?

a. (9.10, 10.90)

b. (9.30, 10.70)

c. (9.45, 10.55)

d. (9.00, 10.50)

Answer 1

We know that the 90% confidence interval for population mean is given by:

(+ Zo. 10/2. C+ Zo.05 (元士 (1.6451- 一元-(1.645)- -9.25, C+ (1.645)- 了。 10.75 n TU

So,

$\overline{x}=10,(1.645)\frac{\sigma}{\sqrt{n}}=0.75\Rightarrow \frac{\sigma}{\sqrt{n}}=\frac{150}{329}$

We know that the 95% confidence interval for population mean is given by:

$\\(\overline{x}\pm Z_{0.05/2}\frac{\sigma}{\sqrt{n}})\\ \\ (\overline{x}\pm Z_{0.025}\frac{\sigma}{\sqrt{n}})\\ \\ (\overline{x}\pm (1.96)\frac{\sigma}{\sqrt{n}})\\ \\ (10\pm (1.96)\frac{150}{329})\\ \\ (10\pm 0.8936)\\ \\(9.10,10.90)$

Hence option A.