Question 1

A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.
A) .4300
B) 2280
C) .5700
D) 4000

Accepted Answer

The point estimate for the proportion is calculated by dividing the number of favorable responses (2280) by the total sample size (4000), which equals 0.5700.

Question 2

Let t0 be a particular value of t. Find a value of $t _ { 0 } \text { such that } P \left( t \leq t _ { 0 } \right) = .005 \text { where } d f = 9 \text {. }$

Accepted Answer

The answer of Let t0 be a particular value of...

Question 3

You are interested in purchasing a new car. One of the many points you wish to consider is  the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $13,200 with a standard deviation of $700. Create a 95% confidence interval for the true mean resale value of a
5-year-old car of that model.

Accepted Answer

The answer of You are interested in purchasing a new...

Question 4

$$\text { For } n = 800 \text { and } \hat { p } = .99 \text {, is the sample size large enough to construct a confidence for } p \text { ? }$$

Accepted Answer

The answer of \[\text { For } n = 800...

Question 5

Let $t _ { 0 }$ be a particular value of $t$. Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

Accepted Answer

The answer of Let $t _ { 0 }$ be...

Question 6

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

A) $15.3 \pm .198$
B) $15.3 \pm .010$
C) $15.3 \pm .013$
D) $15.3 \pm .157$

Accepted Answer

The 95% confidence interval is calculated using the formula: mean ± (Z * (standard deviation/√n)). Here, Z is 1.96 for 95% confidence, standard deviation is 1.6, and n is 250. This gives 15.3 ± 0.198.

Question 7

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many
Students would need to be sampled?
A) 66
B) 1584
C) 3980
D) 6546

Accepted Answer

The answer of A university dean is interested in determining...

Question 8

Suppose you selected a random sample of n = 7 measurements from a normal distribution. 
Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

Accepted Answer

The answer of Suppose you selected a random sample of...

Question 9

For $n = 40 \text { and }\hat { p} = .45 \text {, }$ s the sample size large enough to construct a confidence for p?

Accepted Answer

The answer of For \(n = 40 \text { and...

Question 10

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? 
A) In construction of the confidence interval, a z-value was used.
B) In construction of the confidence interval, a z-value with 20 degrees of freedom was used.
C) In construction of the confidence interval, a t-value with 19 degrees of freedom was used.
D) In construction of the confidence interval, a t-value with 20 degrees of freedom was used.

Accepted Answer

For a sample size of 20, the t-distribution is used with n-1 degrees of freedom, which is 19 in this case.

Question 11

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid?
A) The sample standard deviation is less than the degrees of freedom.
B) None. The Central Limit Theorem applies.
C) The population of total compensations of CEOs in the service industry is approximately normally distributed.
D) The distribution of the sample means is approximately normal.

Accepted Answer

The assumption necessary for the confidence interval to be valid is that the population of total compensations of CEOs in the service industry is approximately normally distributed, especially since the sample size is small (n=18).

Question 12

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean $\mu .$

Accepted Answer

The answer of The following random sample was selected from...

Question 13

The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in  an area and finds 380 in which a firearm was reportedly used. Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

Accepted Answer

The answer of The U.S. Commission on Crime randomly selects...

Question 14

How much money does the average professional football fan spend on food at a single  football game? That question was posed to 43 randomly selected football fans. The sample results provided a sample mean and standard deviation of $16.00 and $2.85, respectively.
Find and interpret a 99% confidence interval for $\mu .$

Accepted Answer

The answer of How much money does the average professional...

Question 15

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences  from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

Accepted Answer

The answer of Suppose (1,000, 2,100) is a 95% confidence...

Question 16

Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the  standard error in this situation be multiplied by a finite population correction factor?
Explain.

Accepted Answer

The answer of Calculate the percentage of the population sampled...

Question 17

The standard deviation of a population is estimated to be 295 units. To estimate the  population mean to within 46 units with 95% reliability, what size sample should be selected?

Accepted Answer

The answer of The standard deviation of a population is...

Question 18

Sales of a new line of athletic footwear are crucial to the success of a newly formed  company. The company wishes to estimate the average weekly sales of the new footwear to within $150 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1500. How many weeks of data must be sampled for the company to get the information it desires?

Accepted Answer

The answer of Sales of a new line of athletic...

Question 19

The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were: $$\begin{array} { l l l l l } 
21.7 & 27.9 & 12.2 & 25.7 & 16.9 \
17.7 & 12.2 & 31.1 & 14.0 & 28.0
\end{array}$$

Find a 99% confidence interval for the standard deviation, ?, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.
A) (0.95, 3.51)
B) (4.24, 14.50)
C) (4.38, 14.50)
D) (4.38, 16.14)

Accepted Answer

The answer of The daily intakes of milk (in ounces)...

Question 20

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$
A) 2.575
B) 2.33
C) 1.645
D) 1.96

Accepted Answer

The answer of What is \(z _ { \alpha /...

Quiz 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

Let t0 be a particular value of t. Find a value of $t _ { 0 } \text { such that } P \left( t \leq t _ { 0 } \right) = .005 \text { where } d f = 9 \text {. }$

$\text { For } n = 800 \text { and } \hat { p } = .99 \text {, is the sample size large enough to construct a confidence for } p \text { ? }$

Let $t _ { 0 }$ be a particular value of $t$ . Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

Suppose you selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

For $n = 40 \text { and }\hat { p} = .45 \text {, }$ s the sample size large enough to construct a confidence for p?

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean $\mu .$

The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain.

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$

Quiz 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

Let t0 be a particular value of t. Find a value of t0 such that P(t≤t0)=.005 where df=9. t _ { 0 } \text { such that } P \left( t \leq t _ { 0 } \right) = .005 \text { where } d f = 9 \text {. }t0​ such that P(t≤t0​)=.005 where df=9.

Let t0t _ { 0 }t0​ be a particular value of ttt . Find a value of t0t _ { 0 }t0​ such that P(t≤t0P \left( t \leq t _ { 0 } \right.P(t≤t0​ or t≥t0)=.1\left. t \geq t _ { 0 } \right) = .1t≥t0​)=.1 where df=\mathrm { df } =df= 14 .

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

Suppose you selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

For n=40 and p^=.45, n = 40 \text { and }\hat { p} = .45 \text {, }n=40 and p^​=.45, s the sample size large enough to construct a confidence for p?

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean μ.\mu .μ.

The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of μc\mu _ { c }μc​

Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain.

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

What is zα/2 when α=0.02?z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?zα/2​ when α=0.02?

Let t0 be a particular value of t. Find a value of $t _ { 0 } \text { such that } P \left( t \leq t _ { 0 } \right) = .005 \text { where } d f = 9 \text {. }$

Let $t _ { 0 }$ be a particular value of $t$ . Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

For $n = 40 \text { and }\hat { p} = .45 \text {, }$ s the sample size large enough to construct a confidence for p?

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean $\mu .$

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$