Question

Past studies have indicated that the percentage of smokers was estimated to be about 30%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 2361 people and found that 664 smoke. Use a 0.05 significance level to test the claim that the percentage of smokers has reduced.

a) Identify the null and alternative hypotheses?

H0H0: Select an answer p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

H1H1: Select an answer p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

• left-tailed
• right-tailed
• two-tailed

c) Identify the appropriate significance level.


d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.


e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.


f) Do you reject the null hypothesis?

• We reject the null hypothesis, since the p-value is less than the significance level.
• We reject the null hypothesis, since the p-value is not less than the significance level.
• We fail to reject the null hypothesis, since the p-value is less than the significance level.
• We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

• There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 30%.
• There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 30%.
• The sample data support the claim that the percentage of smokers is less than 30%.
• There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 30%

Answer 1

The statistic software output for this problem is :

a)

H₀ : p = 0.3
H₁ : p < 0.3

b)

Left tailed

c)

significance level = 0.05

d)

Test statistics = -1.99

e)

P-value = 0.0233

f)

We reject the null hypothesis, since the p-value is less than the significance level.

g)

There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 30%.