Question

In: Statistics and Probability

This semester, there are 259 professors at University A and 128 sent in midterm progress reports....

This semester, there are 259 professors at University A and 128 sent in midterm progress reports. Again, assume the professors at University A are representative of all professors.

(a) Construct a 95% confidence interval for the proportion of all professors who sent in midterm progress reports this semester, and then interpret it. Note: Remember that a confidence interval is made up of three components: pˆ, z, and n. You should have all the information you need to construct the interval.

(b) At CSU San Bernardino, they have 176 professors, of whom 74 sent in midterm progress reports for their students. Is the 95% confidence interval for CSU San Bernardino wider or smaller than the one for University A? Explain answer.

Expert Solution

a) Let X = the number of professor sent in midterm progress from University A.To calculate the confidence interval, you must find , and n , given

x = 128

n =259

is sample proportion.

Since CL = 0.95, then α = 1 – CL = 1 – 0.95 =0.05.

α/2 = 0.025

Then Zc = Zα/2 =Z0.025= 1.96

The corresponding confidence interval is computed as shown below:

b) Let Y = the number of professor sent in midterm progress from CSU San Bernardino.

Given,

y =74

n= 176

The corresponding confidence interval is computed as shown below:

Now, the length of 95% confidence interval for University =0.555 - 0.433

= 0.122

And the length of 95% confidence interval for CSU San Bernardino =0.493 - 0.348

= 0.145

Hence, the 95% confidence interval for CSU San Bernardino wider than the one for University A

orchestra answered 1 year ago

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