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balu736 [363]
2 years ago
10

Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enroll

ed in. The students collect a random sample of 49 students. The mean of the sample is 12. 2 units. The sample has a standard deviation is 1. 6 units. What is the 95% confidence interval for the number of units students in their college are enrolled in? assume that the distribution of individual student enrollment units at this college is approximately normal.
SAT
1 answer:
Andrew [12]2 years ago
4 0

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the number of units students in their college are enrolled in is (11.7, 12.7).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm t\frac{s}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed <em>95% confidence interval</em>, with 49 - 1 = <em>48 df</em>, is t = 2.0106.

Hence:

\overline{x} - t\frac{s}{\sqrt{n}} = 12.2 - 2.0106\frac{1.6}{\sqrt{49}} = 11.7

\overline{x} + t\frac{s}{\sqrt{n}} = 12.2 + 2.0106\frac{1.6}{\sqrt{49}} = 12.7

The 95% confidence interval for the number of units students in their college are enrolled in is (11.7, 12.7).

More can be learned about the t-distribution at brainly.com/question/16162795

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<h3>What is consumer surplus?</h3>

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The complete question goes thus:

For each of three potential buyers of oranges, the table displays the willingness to pay for the first three oranges of the day. Assume Allison, Bob, and Charisse are the only three buyers of oranges, and only three oranges can be supplied per day.

Refer to Table 7-5. If the market price of an orange is $0.65, then consumer surplus amounts to________

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<em>Note that the complete question is found below:</em>

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In conclusion, withdrawal symptoms affect substance abusers.

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