41. Literacy rates Do males have higher average literacy rates than females in Islamic countries? The table below shows the percent of men and women at least 15years old who were literate in 2008in the major Islamic nations. (We omitted countries with populations of less than3million.) Data for a few nations, such as Afghanistan and Iraq, were not available.

Short Answer

Expert verified

The normal and independent requirements are not met.

Step by step solution

01

Given information

Data for a few nations, such as:

Country
Female percent
Male percent
Algeria
66
94
Bangladesh
48
71
Egypt
58
88
Iran
77
97
Jordan
87
99
Kazakhstan
100
100
Lebanon
86
98
Libya
78
100
Malaysia
90
98
Morocco
43
84
Saudi Arabia
79
98
Syria
77
95
Tajikistan
100
100
Tunisia
69
97
Turkey
81
99
Uzbekistan
96
99
Yemen
41
93
02

Explanation

Random, Normal, and Independent requirements for two-sample tmethods is:
The date must be chosen at random. Because the data is of all Islamic nations with populations of more than 3million (excluding Afghanistan and Iraq), having data on more than 10% of all Islamic nations, the Independent criteria is not met.
Furthermore, the samples are not independent, which also contradicts the condition of independence.
The normal requirement is not met because both samples are tiny (less than 30), and the normal probability plot of Male percent has a high curve (reflecting that this distribution is not quite normal).

03

Explanation

Probability plot for women as:

Probability plot for Men as:

The data points of men and female percent are not independent.
As a result, the independent and normal requirements are not met.

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Most popular questions from this chapter

Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag 1has 25%red crackers and Bag 2has 35%red crackers. Each bag contains more than 500crackers. Using a paper cup, your teacher takes an SRS of 50crackers from Bag 1 and a separate SRS of 40crackers from Bag 2. Let p1^-p2^be the difference in the sample proportions of red crackers.

What is the shape of the sampling distribution ofp1^-p2^ ? Why?

A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the 95%confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?

(a) (0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(b) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(c) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(d)(0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(e) (0.44-0.47)±1.96(045)(0.55)1200+1300

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.

Which of the following is the test statistic for the hypothesis test?

(a)t=7.9-92.128

(b)t=9-7.92.128

(c)t=7.9-92.128

(d)t=7.9-92.127

(e)t=9-7.92.127

A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Ask if there is a family history of breast cancer: 3396of the 19,541women in the low-fat group and 4929of the 29,294women in the control group said “Yes.” If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer.

(a) How significant is the observed difference? Carry out an appropriate test to help answer this question.

(b) Describe a Type I and a Type II error in this setting. Which is more serious? Explain.

Based on your answer to Question 3, would you be surprised if the difference in the proportion of red crackers in the two samples was p1^-p^2=-0.02? Explain.

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