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lesantik [10]
3 years ago
13

A class survey in a large class for first-year college students asked, “About how many minutes do you study on a typical weeknig

ht?” The mean response of the 463 students was = 118 minutes with a standard deviation of 65 minutes in the population of all first-year students at this university. Create a 99% confidence interval for the mean study time of all first-year students. Assume all necessary assumptions and conditions apply given the large sample size. Interpret your interval in context.
Mathematics
1 answer:
Anika [276]3 years ago
3 0

Answer:  (110.22, 125.78)

Step-by-step explanation:

The confidence interval for the population mean is given by :-

\mu\ \pm z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}

Given : Sample size = 463

\mu=118\text{ minutes}

\sigma=65\text{ minutes}

Significance level : \alpha=1-0.99=0.01

Critical value : z_{\alpha/2}=z_{0.005}=\pm2.576

We assume that the population is normally distributed.

Now, the 90% confidence interval for the population mean will be :-

118\ \pm\ 2.576\times\dfrac{65}{\sqrt{463}} \\\\\approx118\pm7.78=(118-7.78\ ,\ 118+7.78)=(110.22,\ 125.78)

Hence, 99% confidence interval for the mean study time of all first-year students = (110.22, 125.78)

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