Question

In a random sample of 340 cars driven at low altitudes, 46 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 85 cars driven at high altitudes, 21 of them exceeded the standard. Can you conclude that the proportion of high altitude vehicles exceeding the standard is greater than the proportion of low altitude vehicles exceeding the standard?

a. State whether the test is:

i) a two-sample t-test (independent samples)

ii) a matched pairs

iii) a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list the test statistic the p-value your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

Answer 1

a) iii) a two sample proportion test

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High altitude (1)	Low altitude (2)

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c) Test - stats (z) = 2.22

   P-value = 0.0132

    P-value is less than 0.05

   So, Reject Ho

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d) Since, P-value is less than the significance level so, reject the null hypothesis

we have enough evidence to support the claim that the high altitude proportion is greater than the low altitude proportion

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e)

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	85	21	0.247059
Sample 2	340	46	0.135294

Estimation for Difference

Difference	95% Lower Bound for Difference
0.111765	0.028988

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ > 0

Method	Z-Value	P-Value
Normal approximation	2.22	0.0132