Question

In a program designed to help patients stop smoking, 236 patients were given sustained care, and 84.3% of them were no longer smoking after one month. Use a 0.05 significance level to test the claim that 80% of patients stop smoking when given sustained care. Identify the null and alternative hypotheses for this test. Choose the correct answer below. O A. Ho:p*0.8 H: p=0.8 OB. Ho: P = 0.8 H:p<0.8 @ C. Ho: p = 0.8 H:p*0.8 OD. Ho: p=0.8 H:p>0.8 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is (Round to three decimal places as needed.)

Answer 1

solution:

1)Test hypothesis

H0: p = 0.80

Ha:Ha: p $\neq$ 0.80

Option C is right answer

Test statistics

z = ($\hat{p}$ - p) / sqrt [ p (1 - p) / n]

= ( 0.843 - 0.80) / sqrt( 0.80 * 0.20 / 236)

= 1.651

Two-tailed p-value: 2P(Z > |z|) = 0.0987386

Since p-value > 0.01 level, do not reject H0.

We conclude at 0.01 level that we do not have sufficient evidence to support the claim.

2) Test Hypothesis:

H0: p = 0.80

Ha: p < 0.80

Option D is right answer

Test statistics

z = ($\hat{p}$ - p) / sqrt [ p (1 - p) / n]

= ( 0.760 - 0.80) / sqrt( 0.80 * 0.20 / 96)

= -0.97

p-value :

Left-tailed: P(Z < z) = 0.1660232

Since p-value > 0.05 level, do not reject H0.

We conclude at 0.05 level that we do not have sufficient evidence to support the claim.

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