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castortr0y [4]
3 years ago
7

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time student

s spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the confidence interval at the 95% level of confidence? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)
Mathematics
1 answer:
Butoxors [25]3 years ago
7 0

Answer: (21.541,\ 23.059)

Step-by-step explanation:

The confidence interval for population mean is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n=240 , which is a large sample , so we apply z-test .

Sample mean : \overline{x}=22.3

Standard deviation : \sigma= 6

Significance level : \alpha=1-0.95=0.05

Critical value : z_{\alpha/2}=1.960

Now, a confidence interval at the 95% level of confidence will be :-

22.3\pm(1.960)\dfrac{6}{\sqrt{240}}\\\\\approx22.3\pm0.759\\\\=(22.3-0.759,\ 22.3+0.759)\\\\=(21.541,\ 23.059)

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