Decide whether the normal sampling distribution can be used if can be used, test
ID: 3359436 • Letter: D
Question
Decide whether the normal sampling distribution can be used if can be used, test the claim about the population proportion pat eg ve eve of sanificance using heg en sa pe statistics. Claim: ps 0.43 = 0.10; Sample statistics: p= 0.38, n = 150 Can the normal sampling distribution be used? YA. Yes, because both np and nq are greater than or equal to 5. O B. Yes, because pq is greater than -0.10. ° C. No, because na is less than 5. 0 D. No, because np is less than 5. State the null and alternative hypotheses. Ha p 043 Ho: p = 0.43 Ha: p#043 Ho:p>0.43 Ha p0.43 C) B. C. D. The test cannot be performed.Explanation / Answer
To use the normal sampling distribution, both np and np must be greater then or equal to 5.
Begin by calculating np. The claim p <= 0.46 implies the hypothesized proportion p = 0.46.
np = 150(0.38)
= 57
Next calculate np. First determine the value for q.
q = 1 –p
= 0.62
Use the value of q to find nq.
nq = 150(0.62)
=93
Since both np and nq are greater than or equal to 5, the normal sampling distribution can be used.
The null and alternative hypotheses are given below.
H0;P<=0.43
Ha:P >0.43
the test OF a right-tailed test the level of significance is = 0.05. Find the critical value, rounding to two decimal places.
The critical value is 1.96
Calculate the standardized test statistic z using the following formula.
, z= p^-p /(sqrtpq/n) =0.38-0.43/(sqrt (0.43*0.57/150) =-1.23
The rejection region is shown to the right. If the standardized test statistic falls in the rejection region, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.
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