Class activity
pdf
keyboard_arrow_up
School
Northern Arizona University *
*We aren’t endorsed by this school
Course
MISC
Subject
Philosophy
Date
Feb 20, 2024
Type
Pages
3
Uploaded by GrandGoose2784
Example 1: Is Divorce Morally Acceptable? In a study conducted by the Pew Foundation, we learn that 67% of women in a random sample viewdivorce as morally acceptable. Does this provide evidence that more than 60% of women view divorce as morally acceptable? The standard error for the estimate assuming the null hypothesis is true is 0.021. (a) Null and Alternative Hypotheses: •
H
0 :
p
≤0.60
•
Ha
:
p
>0.60 (b) Standardized Test Statistic: Z=0.67-.60/0.021 Z=3.3333333 (c) P-value: .9996 (d) Conclusion of the Test: we fail to reject the null hypothesis. There is not enough evidence to suggest that more than 60% of women view divorce as morally acceptable based on the sample data. Example 2: Do Men and Women Differ in Opinions about Divorce?
In the same study described above, we find that 71% of men view divorce as morally acceptable. Use this and the information in the previous example to test whether there is a significant difference between men and women in how they view divorce. The standard error for the difference in proportions under the null hypothesis that the proportions are equal is 0.029. (a) What are the null and alternative hypotheses for this test? Ho: P
men
-P
women
=0 Ha: P
men
-P
women
≠0
(b) What is the standardized test statistic? z= SE ( p ^ men − p ^ women )
where p ^ men is the sample proportion of men (71% or 0.71), p ^ women is the sample proportion of women (67% or 0.67), SE SE is the standard error of the difference in proportions (0.029). z = ( 0.71 − 0.67
)/0.029 (c) Use the standard normal distribution to find the p-value. .P-value:.9173 (d) What is the conclusion of the test? we fail to reject the null hypothesis. There is not enough evidence to suggest a significant difference between men and women in how they view divorce based on the sample data. The data does not provide sufficient support to conclude that the proportions of men and women who view divorce as morally acceptable are different. Example 3: Confidence Intervals Three Ways A survey conducted by the Pew Foundation found that 536 of 908 Twitter users say they use Twitter forget news. We wish to find a 95% confidence interval for the proportion of Twitter users who use it to get news. What is the sample statistic? ___536/908 = 0.590__________ • Use percentiles on a bootstrap distribution to find the 95% confidence interval. (0.559 to 0.621). • We can model the bootstrap distribution wi
th a normal distribution with mean equal to the sample statistic and standard deviation equal to the standard error of the bootstrap distribution. Give the mean ___.590_____ and standard deviation ___.016_____ for this normal distribution. Use this normal distribution to find the 95% confidence interval. 0.559 to 0.621 • What is z* for a 95% confidence interval? _
1.96
________ Use the formula “Statistic ± z* · SE” to find the 95% confidence interval. 0.590 ± 1.960 (0.016) 0.590 ± 0.031 0.559 to 0.621 Compare the three answers. They are the same (up to minor variations in the simulations)
Example 4: Obesity in America In Chapter 3, we see that the mean BMI (Body Mass Index) for a large sample of US adults is 27.655. We are told that the standard error for this estimate is 0.009. If we use the normal distribution to find a 99% confidence interval for the mean BMI of US adults: (a) What is z*? 2.575 (b) Find and interpret the 99% confidence interval. 27.655 ± 2.575(0.009) 27.632 to 27.678 We are 99% confident that the mean BMI of all US adults is between 27.632 and 27.678
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help