MATH399N WEEK 8 FINAL EXAM
Q1
Find the area to the right of the z-score 1.40 and to the left of the z-score 1.58 under the standard normal curve.
Use the value(s) from the table above.
Ans:
Q2
Which of the following results in the null hypothesis μ=38 and alternative hypothesis μ<38?
Ans:
A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes.
Q3
On average, Caden has noticed that 17 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 6 trains will pass his house in a 12-hour time period? (Round your answer to three decimal places.)
Ans:
Q4
Liam wants to estimate the percentage of people who lease a car. He surveys 240 individuals and finds that 54 lease a car.
Find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table of common z-scores above.
- Round the final answer to three decimal places.
Ans: margin of error =
Q5
Suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 80% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who are males?
| z0.10 | z0.05 | z0.04 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.751 | 1.960 | 2.326 | 2.576 |
Use the table of values above.
Ans:
Q6
The answer choices below represent different hypothesis tests. Which of the choices are left-tailed tests? Select all correct answers.
Ans:
H0:X=17.3, Ha:X≠17.3
H0:X=19.7, Ha:X<19.7
H0:X=11.2, Ha:X<11.2
H0:X=13.2, Ha:X≠13.2
H0:X=17.8, Ha:X>17.8
Q7
If A and B are events with P(A)=0.3, P(A OR B)=0.82, and P(A AND B)=0.08, find P(B).
Ans:
Q8
A college professor claims the proportion of students that complete a homework assignment is 70%. To test this claim, a random sample of students are monitored and checked if they completed the homework for the algebra class.
Assume that the test statistic for this hypothesis test is −1.73.
Since this is a two tailed hypothesis test, assume that the critical values for this hypothesis test are −1.96 and 1.96.
Come to a decision for the hypothesis test and interpret your results with respect to the original claim.
Ans:
Reject the null hypothesis.
There is enough evidence to reject the claim that the proportion of students that complete a homework assignment is 70%.
Fail to reject the null hypothesis.
There is not enough evidence to reject the claim that the proportion of students that complete a homework assignment is 70%.
Q9
Find the linear regression line for the following table of values. You will need to use a calculator, spreadsheet, or statistical software.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 3 | 6.03 |
| 4 | 9.65 |
| 5 | 11.49 |
| 6 | 11.57 |
| 7 | 12.96 |
| 8 | 14.97 |
| 9 | 16.31 |
| 10 | 17.43 |
| 11 | 18.55 |
Ans:
Q10
The following dataset represents the number of registered students for 60 college courses, sorted and arranged in rows of 5. What is the 50th percentile of the data?
| 5 | 8 | 9 | 9 | 10 |
| 13 | 18 | 19 | 21 | 24 |
| 25 | 26 | 28 | 29 | 30 |
| 33 | 35 | 36 | 43 | 44 |
| 44 | 45 | 47 | 47 | 51 |
| 52 | 54 | 54 | 57 | 57 |
| 57 | 58 | 59 | 59 | 61 |
| 64 | 68 | 70 | 71 | 74 |
| 78 | 78 | 79 | 79 | 81 |
| 82 | 84 | 84 | 86 | 89 |
| 91 | 91 | 92 | 93 | 95 |
| 96 | 96 | 98 | 100 | 100 |
Ans:
Q11
The population standard deviation for the heights of dogs, in inches, in a city is 7.4 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
| z0.10 | z0.05 | z0.04 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.751 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the nearest integer.
Ans:
Q12
Given the following frequency table of values, is the mean or the median likely to be a better measure of the center of the data set?
Ans:
Q13
In which of the following situations can multiple regression be performed? Select all that apply.
Ans:
predicting the current salary of an employee, given the initial salary and the number of years the employee has been in his or her current position
predicting the number of home runs a baseball player will hit in the next season, given the number of home runs the player hit in the previous season and the number of doubles the player hit in the previous season
predicting the number of sodas sold at a concert, given the attendance at a game
predicting the number of cans of chicken noodle soup sold at a supermarket, given the number of flu cases in the past month
Q14
Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary school children and finds that 280 have a social media account.
Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table of common z-scores above.
- Round the final answer to three decimal places.
Ans:
Q15
Determine the critical value or values for a one-mean z-test at the 1% significance level if the hypothesis test is right-tailed (Ha:μ>μ0).
Ans:
−2.326
−2.054
2.054
2.326
−2.054 and 2.054
−2.326 and 2.326
Q16
Hugo is keeping track of the total amount of money he has saved over time. The line graph below shows the data.
How much, in hundreds of dollars, did Hugo save from month 0 to 4?
- Enter the answer as a whole number. For example, if Hugo saved 300 dollars, enter 3 in the box below.
Ans:
Q17
Tanya loves to walk in the park everyday after work. Given the frequency table below for a list of miles walked daily over the past few weeks, find the mean. (Please do not include the units in your answer.)
| Value | Frequency |
| 9 | 2 |
| 10 | 4 |
| 11 | 1 |
| 12 | 2 |
| 13 | 1 |
| 14 | 2 |
| 15 | 2 |
| 16 | 1 |
Ans: mean =
Q18
Timothy wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 75 randomly selected students in the school. What is the statistic?
Ans:
the specific number of siblings for each randomly selected student
the 75 randomly selected students
the mean number of siblings for the randomly selected students
the mean number of siblings for all students in the school
all the students in the school
Q19
A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes?
- Round your answer to 3 decimal places.
Ans:
Q20
A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam.
The following is the setup for this hypothesis test:
{H0:p=0.80Ha:p>0.80
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Ans: test statistic =
Q21
The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. A random sample of 19 houses is taken and results in a sample mean of 1350 square feet.
Find the margin of error for a 80% confidence interval for the population mean.
| z0.10z0.10 | z0.05z0.05 | z0.025z0.025 | z0.01z0.01 | z0.005z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Ans:
Q22
Karen is studying the relationship between the time spent exercising per day and the time spent outside per day and has collected the data shown in the table. The line of best fit for the data is y^=0.16x+45.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.
According to the line of best fit, what would be the predicted number of minutes spent outside for someone who spent 68 minutes exercising? Round your answer to two decimal places, as needed.
Ans:
Q23
The finishing time for cyclists in a race are normally distributed with an unknown population mean and standard deviation. If a random sample of 25 cyclists is taken to estimate the mean finishing time, what t-score should be used to find a 98% confidence interval estimate for the population mean?
Use the portion of the table above or a calculator. If you use a calculator, round your answer to three decimal places.
Ans:
Q24
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs are mutually exclusive.
Select all correct answers.
Ans:
B and C are independent
A and C are mutually exclusive
A and B are independent
A and C are independent
B and C are mutually exclusive
A and B are mutually exclusive
Q25
If A and B are independent events with P(A)=0.5 and P(B)=0.4, find P(A AND B).
Ans:
ANSWERS
Q1
Find the area to the right of the z-score 1.40 and to the left of the z-score 1.58 under the standard normal curve.
Use the value(s) from the table above.
Ans: 0.0237
Q2
Which of the following results in the null hypothesis μ=38 and alternative hypothesis μ<38?
Ans:
A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes.
A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes………..please follow the link below to purchase the solution at $30
