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d1i1m1o1n [39]
3 years ago
5

A publisher reports that 42%42% of their readers own a particular make of car. A marketing executive wants to test the claim tha

t the percentage is actually different from the reported percentage. A random sample of 250250 found that 35%35% of the readers owned a particular make of car. Find the value of the test statistic. Round your answer to two decimal places.
Mathematics
1 answer:
shepuryov [24]3 years ago
6 0

Answer:

z=\frac{0.35 -0.42}{\sqrt{\frac{0.42(1-0.42)}{250}}}=-2.24  

Step-by-step explanation:

Data given and notation  

n=250 represent the random sample taken

\hat p=0.35 estimated proportion of readers owned a particular make of car

p_o=0.42 is the value that we want to test

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that the percentage is actually different from the reported percentage.:  

Null hypothesis:p=0.42  

Alternative hypothesis:p \neq 0.42  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.35 -0.42}{\sqrt{\frac{0.42(1-0.42)}{250}}}=-2.24  

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Answer:

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Step-by-step explanation:

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