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 a using the given sample statistics. Claim: p 0.28; 0.10; Sample statistics: p 0.25, 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 nq is less than 5 O D. Yes, because pq is greater than a 0.10 State the null and alternative hypotheses. O A. Ho: p 30.28 Ha: p 0.28 O B. Ho: p s0.28 Ha: p 0.28 O C. Ho: p20.28 Ha: p

Explanation / Answer

Yes, because both np and nq are greater than or equal to 5

Hypothesis:

H0 : p= 0.28

Ha : p not equal to 0.28

Critical values For 0.10 is 1.64

Test statistic:

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

= sqrt [(0.28 * 0.72) / 132]

= 0.039

z = (pcap - p) /

= (.25 - .28)/0.039

= - 0.769

Now, we need to find p value using z = -0.769

P value = 0.441893.

As p value is greater than significance level 0.10

So, we fail to reject the null hypothesis The data do not provide sufficient evidence to support the claim.

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