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

Question

Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p level of significance using the given sample statistics. Claim: p 0.29; a 0.05; Sample statistics: p 0.25, n 124 Can the normal sampling distribution be used? O A. Yes, because both np and no are greater than or equal to 5. O B. No, because np is less than 5 O C. Yes, because pq is greater than 0.05. O D. No, because ng is less than 5. State the null and alternative hypotheses. O A. Ho p 20.29 H.: D

Explanation / Answer

lets calculate np and np first

np = 124*0.25 = 31

and nq = 124*(1-0.25) = 93 , hence both are greater than 5 , so A

2) The correct answer is B

as we are interested in knowing whether the population stat is 0.29 or not so

H0 : p = 0.29 and

H1 = p |= 0.29

3) The critical value is read from the z table for alpha = 0.05

which is -1.6449

and the z stat is calculated as

= sqrt[ P * ( 1 - P ) / n ]

so sqrt(0.29*(1-0.29)/124) = 0.0407

and z = (p - P) /

so

Z = (0.25 - 0.29)/0.0407 = - 0.982

now as the z stat is less than the z critcal value hence we fail to reject the null hypothesis and conclude that p=0.29 . Hence B , the data point do not provide evidence to support the claim

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