Problem 4: Smoking Bans (25 points) On November 3–5, 2010, the Gallup Organizati
ID: 3155404 • Letter: P
Question
Problem 4: Smoking Bans (25 points) On November 3–5, 2010, the Gallup Organization surveyed 1028 adult Americans and found that 523 said they supported a ban on smoking in public places. More recently, on October 15–17, 2014, the Gallup Organization surveyed 997 adult Americans and found that 550 supported a ban on smoking in public places.
a) Using StatCrunch, find a 90% confidence interval for the difference in the proportion who supported a ban on smoking in 2014 compared to 2010. For this part, just include the table from the StatCrunch output showing the confidence interval.
b) Interpret the confidence interval calculated in Part a in context of the data (as we discussed in class).
c) Using StatCrunch, find a 99% confidence interval for the difference in the proportion who supported a ban on smoking in 2014 compared to 2010. For this part, just include the table from the StatCrunch output showing the confidence interval.
d) Interpret the confidence interval calculated in Part c in context of the data (as we discussed in class).
e) Using = 0.05, is there evidence to conclude that the proportion who support a ban on smoking in public places has increased over time?
i) State the null and alternative hypotheses.
ii) State the significance level for this problem.
iii) Check whether the conditions allowing use of the standard Normal distribution to compute p-values are satisfied.
iv) Give the probability notation statement for the p-value.
v) Use StatCrunch to compute the test statistic and p-value. Copy the table from the StatCrunch output showing the test statistic and p-value into your solutions document.
vi) State whether you reject or do not reject the null hypothesis.
vii) State your conclusion in context of the problem (i.e. interpret your results).
Explanation / Answer
Here we are given that,
x1 = 523
n1 = 1028
x2 = 550
n2 = 997
Using = 0.05, is there evidence to conclude that the proportion who support a ban on smoking in public places has increased over time?
i) State the null and alternative hypotheses.
Here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 > p2
where p1 and p2 are population proportions.
ii) State the significance level for this problem.
level of significance = alpha = 0.05
This we can done using TI-83 calculator.
steps :
STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input values --> select alternative ">p2" --> Calculate --> ENTER
Results :
Test statistic Z = -1.9337
P-value = 0.9734
But the test is right sided therefore
P-value = 1 - 0.9734 = 0.03
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : Is there evidence to conclude that the proportion who support a ban on smoking in public places has increased over time.
90% confidence interval for difference in proportion is :
TI-83 steps for confidence interval :
steps :
STAT --> TESTS --> 8:2-PropZInt --> Input all the values --> C-level = 0.90 --> Calculate --> ENTER
90% confidence interval for difference in proportion is (-0.0794, 0.0064).
99% confidence interval for difference in proportion is ( -0.1, 0.01419).
We are 90% confident that the difference in population proportion is lies between -0.0794 and 0.0064.
We are 99% confident that the difference in population proportion is lies between -0.1 and 0.01419.
Statcrunch commands for confidence interval and difference im proportion is :
1. If you have raw data, enter them into the spreadsheet. Name each column variable.
2. Select Stat, highlight Proportions, select Two sample, and then choose either with data or with summary.
3. If you chose with data, select the column that has the observations, choose which outcome represents a success for each sample, then click Next>. If you chose with summary, enter the number of successes and the number of trials for each sample. Click Next>.
4. If you choose the hypothesis test radio button, enter the value of the proportion stated in the null hypothesis and choose the direction of the alternative hypothesis from the pull-down menu. If you choose the confidence interval radio button, enter the level of confidence. Click Calculate.