Question

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.

Answer 1

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

Sol iwen o-8S 273 300 oppucalle 0 02 うFw ơAucbS → ρ r alne Co.on) < 0,025 :. Rdg Ayontー

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