Question

Past studies have indicated that the percentage of smokers was estimated to be about 35%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 2376 people and found that 784 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: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

H1H1: ? 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 35%.
• There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 35%.
• The sample data support the claim that the percentage of smokers is less than 35%.
• There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 35%

Answer 1

Please do the comment for any doubt or clarification. Please upvote if this helps you out. Thank You!

a)Identify the null and alternative hypotheses?

Null Hypothesis, H0: p = 0.35
Alternative Hypothesis, Ha: p < 0.35

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

Left Tailed

c) Identify the appropriate significance level.

0.05

d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.
Test Statistic= -2.05

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.
P value=0.0203 or try this if this is incorrect 0.0202

f) Do you reject the null hypothesis?

We reject the null hypothesis since the p-value is 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 35%.

Using Excel<data<megastat<hyothesis test

Observed	Hypothesized
0.33	0.35	p (as decimal)
784/2376	832/2376	p (as fraction)
784.	831.6	X
2376	2376	n
	0.0098	std. error
	-2.05	z
	.0203	p-value (one-tailed, lower)
	0.3111	confidence interval 95.% lower
	0.3489	confidence interval 95.% upper
	0.0189	margin of error