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 alpha using the given sample statistics. Claim: p is not equal to 0.22; Alpha = 0.01; Sample statistics: p = 0.15, n = 180Can the normal sampling distribution be used? A. No, because np is less than 5. B. No, because nq is less than 5. C. Yes, because both np and nq are greater than or equal to 5. D. Yes, because pq is greater than alpha = 0.01. State the null and alternative hypotheses. Determine the critical value(s).Find the z-test statistic.

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-12-26T04:50:43+01:00

Answer:

A

The correct option is C

B

The value of z-test is [tex]z = -2.267[/tex]

Step-by-step explanation:

From the question we are told that

The null hypothesis [tex]H_o : p = 0.22[/tex]

The alternative hypothesis [tex]H_a : p \ne 0.22[/tex]

The level of significance is [tex]\alpha = 0.01[/tex]

The sample proportion is [tex]\^ p = 0.15[/tex]

The sample size is n = 180

Generally from central limit theorem

if np and nq are > 5 then normal sampling distribution can be used

So

np = 180 * 0.22 = 39.6 > 5

and

nq = 180 * (1 -0.22) = 140.4 > 5

So normal sampling distribution can be used

Generally the z-test is mathematically represented as

[tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1- p ) }{n } } }[/tex]

=> [tex]z = \frac{ 0.15 - 0.22 }{ \sqrt{\frac{ 0.2(1- 0.22 ) }{ 180 } } }[/tex]

=> [tex]z = -2.267[/tex]