# A medical researcher says that less than #25%# of US. adults are smokers. In a random sample of #200# US. adults, #18.5%# say that they are smokers. At #alpha = 0.05#, is there enough evidence to reject the researchers claim?

The medical researcher's expectation is wrong. There is enough statistical evidence to prove that 25% or more are smokers in the university.

It is about testing the significance of sample Proportions.

Population Parameter

P = 25% [Population Proportion}

Sample Statistic

p=18.5% [sample Proportions]

Significance level 0.05

Sample size

Distribution to be used : Normal Distribution [since

#H_O:P>=25%#

#H_1:P<25%#

[Tips : We are going to compare Calculated

Calculations:

Table Value (

In our case table value is

Since left tail test is used the actual Table value is

Refer the image.

Calculated

Here

#SE=sqrt(200 xx 0.25 xx 0.75)=6.124#

#z=(18.5-25)/6.124=(-6.5)/6.124=-1.06#

Conclusion:

Since the calculated value

Inference:

There is enough statistical evidence to prove that 25% or more are smokers in the university.

It means, the medical researcher's expectation is wrong.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A medical researcher says that less than #25%# of US. adults are smokers. In a random sample of #200# US. adults, #18.5%# say that they are smokers. At #alpha = 0.05#, is there enough evidence to reject the researchers claim?
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