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 the appropriate null and alternate hypotheses.b. Compute the value of the test statistic.c. State a conclusion at the a=0.01 level of significance.

Question
Asked Nov 4, 2019

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 the appropriate null and alternate hypotheses.

b. Compute the value of the test statistic.

c. State a conclusion at the a=0.01 level of significance.

check_circleExpert Solution
Step 1

Given Data

Low altitude
46
= 0.1353
340
n1 340, X1 46, p, = i.
п1
11
High altitude
21
= 0.2471
85
x2
85, x2= 21, p2
П2
n2
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Low altitude 46 = 0.1353 340 n1 340, X1 46, p, = i. п1 11 High altitude 21 = 0.2471 85 x2 85, x2= 21, p2 П2 n2

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Step 2

a)

Formulation of Hypotheses:

The aim is to check whether the proportion of high altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard

The null hypothesis is:

H0­ : p1 = p2, that is, there is no difference in the proportion of high altitude vehicles and proportion of low-altitude vehicles

The alternative hypothesis is:

H1 : p1&n...

Pooled proportion is given by
46 21
Х1+ х2
p =
= 0.1576
340 85
Пу + п2
(Ф, — Ра) — (р1 — р2)
0.1353 0.2471
= -2.530
= Z
0.1576(1 0.1576) x (40
85
п2.
Calculation of z-critical
NORM.S.INV(0.01))
-2.326(From Excel =
Zo.01
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Pooled proportion is given by 46 21 Х1+ х2 p = = 0.1576 340 85 Пу + п2 (Ф, — Ра) — (р1 — р2) 0.1353 0.2471 = -2.530 = Z 0.1576(1 0.1576) x (40 85 п2. Calculation of z-critical NORM.S.INV(0.01)) -2.326(From Excel = Zo.01

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