APU MATH530 2021 March Quiz 3 Latest

MATH530 Applied Statistics

Quiz 3

Question 1 Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.7 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.7 seconds. What would you use for the null hypothesis?

Question options:

\f$\mu  > 6.7 seconds\f$

\f$\mu  = 6.7 seconds\f$

\f$\mu  < 6.7 seconds\f$

\f$\mu  \neq  6.7 seconds\f$

Question 2 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation \f$\sigma  =\f$   2.8%. Now, suppose we wish to test the null hypothesis that \f$\mu  =\f$ 6.4% against the alternative that \f$\mu  >\f$ 6.4% using a level of significance of \f$\alpha =\f$ .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of \f$\bar{x} =\f$ 8.91%.What is the value of the test statistic?

Question options:

-0.224

-3.586

3.586

0.896

Question 3 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation \f$\sigma  =\f$ 2.8%. Now, suppose we wish to test the null hypothesis that \f$\mu  =\f$  6.4% against the alternative that \f$\mu  >\f$  6.4% using a level of significance of \f$\alpha  =\f$  .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of \f$\bar{x} = \f$  8.91%.  What is the p-value associated with this test?

Question options:

.0002

.0500

.0100

.0068

Question 4 Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation \f$\sigma  = 2.4\f$ % . A random sample of 19 Australian bank stocks has a sample mean of \f$\bar{x} \f$  = 8.71%. For the entire Australian stock market, the mean dividend yield is \f$\mu \f$  = 5.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9%? Use \f$\alpha \f$  = .05. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?

Question options:

The p-value is less than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.

The p-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

The p-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

The p-value is greater than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.

The p-value is less than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

Question 5 Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 397 numerical entries from the file and r = 110 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using \f$\alpha  =\f$  0.1. What is the value of the test statistic?

Question options:

20.704

0.052

-20.704

-0.052

-1.039

Question 6 Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 463 numerical entries from the file and r = 122 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using \f$\alpha  =\f$   0.1. What is the P-value of the test statistic?

Question options:

0.921

0.039

0.020

0.961

0.079

Question 7 A random sample of n1 = 16 communities in western Kansas gave the following rates of hay fever per 1000 population for people under 25 years of age.

121

115

124

99

134

121

110

116

113

96

116

116

135

96

96

116

 

A random sample of n2 = 14 communities in western Kansas gave the following rates of hay fever per 1000 population for people over 50 years old.

113

86

106

102

113

94

94

108

103

99

78

105

88

100

 

Assume that the hay fever rate in each age group has an approximately normal distribution. Using the method outlined in Brase and Brase, do the data indicate that the age group over 50 has a lower rate of hay fever? Use \f$\alpha  =\f$ 0,05.  Do you reject or fail to reject the null hypothesis? Are the data statistically significant at the \f$\alpha  =\f$ 0.05  level of significance?

Question options:

Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis.

Since the p-value is less than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis.

Since the p-value is greater than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.

Since the p-value is less than the level of significance, the data are statistically significant. Thus, we reject the null hypothesis.

Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we reject the null hypothesis.

Question 8 It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

x	5.25	5.50	5.75	6.25	6.50
y	12	38	38	42	59

 

Find the equation of the least squares line \f$\hat{y} = a + bx\f$

Question options:

y^=−130.081+28.698x

y^=130.081−28.698x

y^=130.081+28.698x

y^=28.698−130.081x

Question 9 It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

x	5.25	5.50	5.75	6.25	6.50
y	12	38	38	42	59

 

What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?

Question options:

0.6%

2.3%

78.2%

84.8%

7.9%

Question 10  It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

x	5.25	5.50	5.75	6.25	6.50
y	12	38	38	42	59

 

Calculate the sample correlation coefficient r.

Question options:

-0.884

-0.821

0.884

0.091

0.909