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Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores. Using their data, each student constructs a 90% confidence interval for μ the average quiz score of the 5000 students. Which one of the following conclusions is correct?

A. The widths of the 110 confidence intervals will be equal.

B. About 10% of the sample means will not be included in the confidence intervals.

C. About 90% of the confidence intervals will contain µ.

D. About 90% of the data will be found in these confidence intervals.

Respuesta :

Answer:

C

Step-by-step explanation:

In this question, we are asked to select which of the options best answer the question.

We proceed as follows;

Using the information given,

Each of the 110 students in a statistics class selects a random sample of 35 Quiz scores

from a population of 5000 scores. They are not given the population mean and standard deviation.

Now, using these data, each student then construct a 90% confidence interval for µ which is the average Quiz score in the population of 5000 students.

By definition, the population mean values will definitely be within the limits of this

confidence interval.

Thus, the correct answer is, Option (c)

Using the t-distribution, it is found that the correct option is given by:

C. About 90% of the confidence intervals will contain the population mean.

Each student will have access to the sample standard deviation, hence the t-distribution will be used.

The interval is given by:

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

In which:

  • [tex]\overline{x}[/tex] is the sample mean, which will be different for each student.
  • t is the critical value, which will be the same for all students, as it is a 90% confidence interval with 35 - 1 = 34 df.
  • s is the sample standard deviation, which also will be different for each student.
  • n is the sample size, which is [tex]n = 35[/tex] for all students.

The width of the interval is:

[tex]W = 2t\frac{s}{\sqrt{n}}[/tex]

Since they will have different values of s, they will have different widths.

The interpretation of a x% confidence interval is that about x% will contain the population mean, hence, option c is correct.

A similar problem is given at https://brainly.com/question/15180581

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