Question

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

Answer 1

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.