Decide whether the normal sampling distribution can be used. If it can be used, test the...

Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance ? using the given sample statistics.

Claim: p?0.27 ?=0.10 ; Sample statistics: ModifyingAbove p =0.26 , n=150

Solutions

Expert Solution

Conditions for normal distribution

we have n = 150 and p = 0.26

so, np = 150*0.26 = 39 greater than or equal to 10 and 150*(1-0.26) = 111 greater than or equal to 10

So, conditions for normal sampling distribution are met.

Hypothesis testing

Null hypothesis: p = 0.27

Alternate hypothesis:

Calculation for test statistics

z =

setting

we get

z statistics =

Using the normal distribution, we can get the p value corresponding to the calculated z value

P value = 0.7795

It is clear that 0.7795 is greater than 0.10 alpha level

Thus, we fail to reject the null hypothesis because the p value is insignificant

We can conclude that we dont have enough evidence to support the given claim.

orchestra answered 1 year ago

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