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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 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 :

Answer:

( 11.7 , 12.7 )

Step-by-step explanation:

The provided information is:

Sample mean = [tex]\bar{X} = 12.2[/tex]

Standard deviation = [tex]\sigma=1.6[/tex]

Sample size = n = 49

Significance level = [tex]\alpha=0.05[/tex]

Thus, the 95% confidence interval is:

[tex]\bar{X}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\=12.2\pm Z_{0.05/2}\frac{1.6}{\sqrt{49}}\\=12.2\pm 1.96\times0.2286\\=12.2\pm 0.4480\\=(11.7.12.7)[/tex]