Let p equal the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law. It was claimed that p = 0.14. An advertising campaign was conducted to increase this proportion. Two months after the campaign, y = 104 out of a random sample of n = 590 drivers were wearing their seat belts . Was the campaign successful? (a) Define the null and alternative hypotheses. (b) Define a rejection region with an α = 0.01 significance level. (c) Determine the approximate p-value and state your conclusion.

a)Null hypothesis:  

Alternative hypothesis:  

b) For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

So then the rejection region would be

c) The significance level provided . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

Step-by-step explanation:

Data given and notation

n=590 represent the random sample taken

X=104 represent the drivers were wearing their seat belts

We can estimate the sample proportion like this:

estimated proportion of  drivers were wearing their seat belts

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

a) System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of drivers were wearing their seat belts is higher than 0.14 or no, so the system of hypothesis are.:  

Null hypothesis:  

Alternative hypothesis:  

Part b

For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

So then the rejection region would be

Part c

The statistic is given by:

(1)  

Calculate the statistic  

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

Statistical decision  

The significance level provided . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

42%

step-by-step explanation:

we know,

total people = 60

total males = 25

percentage of males

= 25/60 × 100

= 25/6 × 10

= 25/3 × 5

= 125 / 3

= 41.

rounding of = 42%

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the answer is 62.8 cubic units