# 19, A website reported that 85% of personal computers run a Windows operating system, 10% ru n a Mac operating system, and 5% are running an operating system other than Windows or Mac. Suppose in…

19, A website reported that 85% of personal computers run a Windows operating system, 10% ru n a Mac operating system, and 5% are running an operating system other than Windows or Mac. Suppose in a random sample of 300 personal computers it was found that 273 cf them are running Windows, 21 are using a Mac operating system, and 6 are running something other than Windows or Mac. Do the sample data provide evidence that the website's reported percentages are incorrect? Test the relevant hypotheses using a significance level of α 0.025.

## Solutions

##### Expert Solution

Below is the results of – detail test is followed after
that.

a.)

Test and CI for One Proportion

Method

 p: event proportion Normal approximation method is used for this analysis.

Descriptive Statistics

 N Event Sample p 97.5% CI for p 300 273 0.910000 (0.872966, 0.947034)

Test

 Null hypothesis H₀: p = 0.85 Alternative hypothesis H₁: p ≠ 0.85
 Z-Value P-Value 2.91 0.004

b.)

Test and CI for One Proportion

Method

 p: event proportion Normal approximation method is used for this analysis.

Descriptive Statistics

 N Event Sample p 97.5% CI for p 300 21 0.070000 (0.036982, 0.103018)

Test

 Null hypothesis H₀: p = 0.1 Alternative hypothesis H₁: p ≠ 0.1
 Z-Value P-Value -1.73 0.083

c).

Test and CI for One Proportion

Method

 p: event proportion Normal approximation method is used for this analysis.

Descriptive Statistics

 N Event Sample p 97.5% CI for p 300 6 0.020000 (0.001883, 0.038117)

Test

 Null hypothesis H₀: p = 0.05 Alternative hypothesis H₁: p ≠ 0.05
 Z-Value P-Value -2.38 0.017