Mathematics, 12.08.2020 07:01 dlatricewilcoxp0tsdw

In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

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The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.

Step-by-step explanation:

We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.

In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.

Let p_1 = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.

p_2 = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.

So, Null Hypothesis, H_0 : $p_1\leq p_2$ {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}

Alternate Hypothesis, H_A : p_1p_2 {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}

The test statistics that will be used here is Two-sample z-test statistics for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = $\frac{24}{90}$ = 0.27

$\hat p_2$ = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = $\frac{42}{380}$ = 0.11

n_1 = sample of cars driven at high altitudes = 90

n_2 = sample of cars driven at low altitudes = 380

So, the test statistics = $\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }$

= 3.234

The value of z-test statistics is 3.234.

Answer from: Quest

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Answer from: Quest

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base

For my math finals respond asap! the figure in the center of the net has four congruent sides. what

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