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

Respuesta :

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).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

  • [tex]\overline{x}[/tex] 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 95% confidence interval, with 49 - 1 = 48 df, is t = 2.0106.

Hence:

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

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

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 https://brainly.com/question/16162795

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