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 at the given level of significance o using the given sample statistics. Claim: p 0.28; 0.10; Sample statistics: pa0.25, n 132 Can the normal sampling distribution be used? o A. No, because np is less than 5 O B. Yes, because both np and nq are greater than or equal to 5. O C. No, because ng is less than 5 O D. Yes, because pq is greater than 0.10. State the null and alternative hypotheses. O A. Ho: p 0.28 Ha: p 0.28 O B. Ho: ps0.28 Ha: p 0.28 O C. Ho p20.28 Ha: p

Explanation / Answer

1.

Answer is B. np and np are both more than 5, therefore you can use it.

np = .25*132 = 33
nq = .75*132 = 99

2.

Null Hypothesis: H0: Mu = .28
Alt. Hypothesis: H0: Mu !=.28

3.

Z = +/- 1.645

4.

Zstat = (.25-.28)/(sqrt(.28*.72/132) = -.77

5.
-1.645<Zstat<1.645

So, Zstat lies between critical values. Hence, Ho cant be rejected due to lackof evidence.

Fail to reject H0. The data doesn't provide sufficient evidence to support the claim

Answer is A

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