Business STAT Week 8 Exam (2016) - The exact spread of the t distribution depends on the

The exact spread of the t distribution depends on the _________

		Standard deviation of the sample
		Sample size n
		Number of degrees of freedom
		z distribution

1.5 points

Question 2

The width of a confidence interval will be

		Narrower for 99 percent confidence than 95 percent confidence
		Wider for a sample size of 100 than for a sample size of 50
		Narrower for 90 percent confidence than 95 percent confidence
		Wider when the sample standard deviation (s) is small than when s is large

1.5 points

Question 3

In a manufacturing process, a random sample of 9 bolts has a mean length of 5 inches with a variance of .09. What is the 90 percent confidence interval for the true mean length of the bolt?

		4.8355 to 5.1645
		4.5065 to 5.4935
		4.8140 to 5.1860
		4.9320 to 5.2743

2.5 points

Question 4

In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 4 inches with a standard deviation of .2 inches. What is the 95 percent confidence interval for the true mean length of the bolt?

		3.8463 to 4.1537
		4.5065 to .54935
		4.7690 to 5.2310
		5.4420 to 6.5580

2.5 points

Question 5

When determining the sample size, if the value found is not an integer initially, you should ____________ choose the next highest integer value.

		Always
		Sometimes
		Never

1.5 points

Question 6

When the population is normally distributed, population standard deviation ? is unknown, and the sample size is n = 15; the confidence interval for the population mean ? is based on:

		The z (normal) distribution
		The t distribution
		The Poisson distribution
		None of these

1.5 points

Question 7

There is little difference between the values of t?/2 and z?/2 when:

		The sample size is small
		The sample size is large
		The sample mean is small
		The sample mean is large

1.5 points

Question 8

If everything else is held constant, decreasing the margin of error causes the required sample size to ____________

		Stay the same
		Decrease
		Increase

1.5 points

Question 9

When sample size is 24, fint t.10

		1.325
		1.323
		1.321
		1.319

2.5 points

Question 10

When sample size is 15, find t.025

		2.145
		2.131
		2.120
		2.110

2.5 points

Question 11

When sample size is 5, find t.001

		10.215
		7.173
		5.893
		5.208

2.5 points

Question 12

Researchers have studied the role that the age or workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are:

Age Groug

18-24 25-44 45-64

Mean 4.17 4.04 4.31

Std Dev 0.75 0.81 0.82

N 241 768 677

Construct a 95 percent confidence interval for the mean hours spent on personal tasks for 45-64 year olds.

		[4.10, 4.19]
		[4.19, 4.28]
		[4.25, 4.37]
		[4.38, 4.44]

2.5 points

Question 13

Researchers have studied the role that the age or workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are: Age Groug 18-24 25-44 45-64 Mean 4.17 4.04 4.31 Std Dev 0.75 0.81 0.82 N 241 768 677 Construct a 90 percent confidence interval for the mean hours spent on personal tasks for 25-44 year olds.
		[3.72, 4.00]
		[3.83, 4.03]
		[3.92, 4.04]
		[3.99, 4.09]

2.5 points

Question 14

Researchers have studied the role that the age or workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are: Age Groug 18-24 25-44 45-64 Mean 4.17 4.04 4.31 Std Dev 0.75 0.81 0.82 N 241 768 677 Construct a 99 percent confidence interval for the mean hours spent on personal tasks for 18-24 year olds.
		[3.99, 4.12]
		[4.02, 4.15]
		[4.04, 4.24]
		[4.05, 4.29]

2.5 points

Question 15

Researchers have studied the role that the age or workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are:

Age Groug

18-24 25-44 45-64

Mean 4.17 4.04 4.31

Std Dev 0.75 0.81 0.82

N 241 768 677

Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 year olds.

		[3.97, 4.11]
		[3.99, 4.14]
		[4.02, 4.19]
		[4.05, 4.22]

2.5 points

Question 16

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. In 1996, the average LOS for non-heart patients was 4.6 days. A random sample of 25 hospitals in one state had a mean LOS for non-heart patients in 2000 of 3.8 days and a standard deviation of 1.4 days. Calculate a 95 percent confidence interval for the population mean LOS for non-heart patients in these hospitals in 2000.

		[3.24, 4.36]
		[3.22, 4.38]
		[3.34, 4.26]
		[3.27, 4.33]

2.5 points

Question 17

The coffee and soup machine at the local bus station is supposed to fill cups with 6 ounces of soup. 5 cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.12 ounces. Construct a 99 percent confidence interval for the true machine-fill amount.

		[5.75, 5.99]
		[5.85, 6.05]
		[5.90, 6.00]
		[5.68, 6.18]

2.5 points

Question 18

An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas. They test a sample of 10 cars and obtain a mean of 22.4 miles. Assuming that the standard deviation is 2.7 miles, find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.

		[20.47, 24.33]
		[20.70, 35.70]
		[24.85, 31.55]
		[25.83, 30.57]

2.5 points

Question 19

A sociologist develops a test designed to measure attitudes about disabled people and gives the test to 22 randomly selected subjects. Their mean score is 71.2 with a standard deviation of 9.5. Construct the 98 percent confidence interval for the mean score of all subjects.

		[60.26, 90.14]
		[63.46, 78.94]
		[66.10, 76.30]
		[63.21, 79.19]

2.5 points

Question 20

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected.

True

False

1.5 points

Question 21

A Type I error is rejecting a true null hypothesis

True

False

1.5 points

Question 22

The larger the p-value, the more we doubt the null hypothesis

True

False

1.5 points

Question 23

A Type II error is failing to reject a false null hypothesis

True

False

1.5 points

Question 24

When testing a hypothesis about a single mean, if the sample size is 51, and the population standard deviation is known, the correct test statistic to use is ___________

		r
		z
		t
		p-value

1.5 points

Question 25

When testing a hypothesis about a single mean, if the sample size is 20, the population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is __________

		r
		z
		t
		p-value

1.5 points

Question 26

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis

		p = .66
		p > .66
		p < .66
		p ? .66

2 points

Question 27

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. The alternative hypothesis is

		p < .66
		p > .66
		p = .66
		p ? .66

2 points

Question 28

The dependent variable is the variable that is being described, predicted, or controlled

True

False

1.5 points

Question 29

The dependent variable is the variable that is being described, predicted, or controlled.

True

False

1.5 points

Question 30

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

True

False

1.5 points

Question 31

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable

True

False

1.5 points

Question 32

When using simple regression analysis, if there is a strong correlation between the independent and dependent variables, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

True

False

1.5 points

Question 33

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

True

False

1.5 points

Question 34

The least squares regression line minimizes the sum of the

		Differences between actual and predicted Y values
		Absolute deviations between actual and predicted Y values
		Absolute deviations between actual and predicted X values
		Squared differences between actual and predicted Y values
		Squared differences between actual and predicted X values

2 points

Question 35

The point estimate of the variance in a regression model is

		SSE
		b0
		MSE
		b1

2 points

Question 36

In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) ___________ have the same sign

		Always
		Sometimes
		Never

2 points

Question 37

The _____________ measures the strength of the linear relationship between the dependent variable and the independent variable

		Correlation coefficient
		Distance value
		Y-intercept
		Residual

2 points

Question 38

The correlation coefficient may assume any value between

		0 and 1
		- ? and ?
		0 and 8
		-1 and 1

2.5 points

Question 39

In simple regression analysis, if the correlation coefficient is a positive value, then

		The Y intercept must also be a positive value
		The coefficient of determination can be either positive or negative, depending on the value of the slope
		The least squares regression equation could either have a positive or a negative slope
		The slope of the regression line must also be positive

2.5 points

Question 40

The simple linear regression (least squares method) minimizes

		SSyy
		Total variation
		SSxx
		SSE

2.5 points

Question 41

The following results were obtained from a simple regression analysis:

? = 37.2895 - 1.965X
r2 = .6744 sb = .2934

For each unit change in X (independent variable), what is the estimated change in Y (dependent variable)?

		-1.965
		37.2895
		.6744
		.2934

3 points

Question 42

The following results were obtained from a simple regression analysis:

? = 37.2895 - 1.2024X
r2 = .6744 sb = .2934

When X (independent variable) is equal to zero, what is the estimated value of Y (dependent variable)?

		.2934
		.6744
		- 1.2024
		37.2895

3 points

Question 43

The following results were obtained from a simple regression analysis:

? = 37.2895 - (1.2024)X
r2 = .6744sb = .2934

What is the proportion of the variation explained by the simple linear regression model?

		37.2895
		- 1.2024
		.6744
		.2934

3 points

Question 44

Use the following problem to solve questions 44, 45, 46 and 47. Refer to the textbook page 476, Table 13.3 for data.

Enterprise Industries produces Fresh, a brand of liquid laundry detergent. In order to study the relationship between price and demand for the large bottle of Fresh, the company has gathered data concerning demand for Fresh over the last 30 sales periods ( each sales period is four weeks). Here, for each sales period,

y = demand for the large bottle of Fresh ( in hundreds of thousands of bottles) in the sales period, and

x = the difference between the average industry price ( in dollars) of competitors’ similar detergents and the price ( in dollars) of Fresh as offered by Enterprise Industries in the sales period.

Question a. Find the least square point estimates b0 and b1:

		b0 = 2.665 and b1 = 7.814
		b0 = 7.814 and b1 = 2.665
		b0 = 9.52 and b1 = .60
		b0 = 9.00 and b1 = .50

3 points

Question 45

Question b. Interpret b0 and b1:

		b0 = a $7.814 price difference yields an estimated demand of 0 b1 = each increase in $1 of price difference increases estimated demand on average by 2.665 which means 266,500 bottles
		b0 = a $0 price difference yields an estimated demand of 7.814 b1 = each increase in $2.665 of price difference increases estimated demand on average by 1 which means 266,500 bottles
		b0 = a $0 price difference yields an estimated demand of 7.814 b1 = each increase in $1 of price difference increases estimated demand on average by 2.665 which means 266,500 bottles
		b0 = a $0 price difference yields an estimated demand of 0 b1 = each increase in $1 of price difference increases estimated demand on average by 2.665 which means 266,500 bottles

3 points

Question 46

Which one represent the correct equation of the least squares line for this problem?

		y-hat = b0 + b1x = 7.814 + x
		y-hat = b0 + b1x = 1 + 2.665x
		y-hat = b0 + b1x = 2.665 + 7.814x
		y-hat = b0 + b1x = 7.814 + 2.665x

3 points

Question 47

What is the point estimate of the mean demand in all sales periods when the price difference is $ 0.28

		1,077,900
		781,400
		856,020
		266,500

3 points

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