Question

In a program designed to help patients stop smoking, 203 patients were given sustained care, and 80.8 % of them were no longer smoking after one month. Use a 0.01

significance level to test the claim that 80 % of patients stop smoking when given sustained care.

Part A) Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H₀: p = 0.8, H₁ :p ≠ 0.8

B. H₀: p=0.8, H₁ : p > 0.8

C. H₀: p ≠ 0.8, H₁ : p = 0.8

D. H₀: p = 0.8, H₁ : p < 0.8

Part B) Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

(Round to two decimal places as needed.)

Part C) Identify the P-value for this hypothesis test.

The P-value for this hypothesis test is

(Round to three decimal places as needed.)

Identify the conclusion for this hypothesis test.

A. Reject H0 . There is not sufficient evidence to reject the claim that 80 % of patients stop smoking when given sustained care.

Answer 1

Part A) H₀: p = 0.8, H₁ : p ≠ 0.8. Part B) The test statistic for this hypothesis test is Z. Part C) The P-value for this hypothesis test is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

Step-by-step explanation:

Part A) The null hypothesis is H₀: p = 0.8, and the alternative hypothesis is H₁ : p ≠ 0.8. This means that the claim is that the proportion of patients who stop smoking when given sustained care is 80%, and we want to test if the proportion is different from 80%.

Part B) The test statistic for this hypothesis test is Z, which follows a standard normal distribution.

Part C) The P-value for this hypothesis test is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true. To calculate the P-value, we would need the observed test statistic value and the critical value.