Chapter 6
Find the probability.
P(Z < 1.67)
.9525
Find the Z critical value of a 95% confidence interval.
1.960
Write the null and alternative hypothesis.
A chemist invents an additive to increase the average life of an automobile battery. The mean lifetime of a battery without the additive is 34 months.
H0: µ = 34
H1: µ > 34
True or False: Assumptions between two means when using the Z test consists of the sample being random and independent.
True
Is a correlation coefficient of -.78 or .32 stronger?
-.78. Although its negative, it's still a stronger, linear relationship.
Find the value of z0
P(Z < z0) = .2266
-0.75
Find the T critical value for a 90% confidence interval for a sample size of 13.
+ and - 1.782
What kind of error is committed when the null hypothesis is true and it gets rejected?
Type I error
When using a T-test, do we use s or Sp2 when the population standard deviations are NOT equal to eachother?
We use s, or the sample standard deviation.
Find the correlation coefficient. (Mis. As. - Missing Assignments)
Student: A B C D E F G H I J K L
Mis. As: 2 0 2 1 7 8 4 6 1 0 3 4
Grade: 87 98 82 92 61 55 78 80 88 100 43 79
-.708
An adult has on average 4.7 cups of coffee a day. Assuming the variable is normally distributed and has a standard deviation of 0.2, find the percentage of people who have less than 5.3 cups of coffee a day.
.9987 or 99.87%
A researcher wishes to estimate the average number of automobile thefts in a large city within 3 automobiles. He wishes to be 95% confident, and the standard deviation was found to be 4.7. How many days should she select to survey?
10 days
Find the T critical value for a = 0.05 in a left tailed test with a sample size of 23.
-1.717
A study of two random samples, with 26 people each, found that the average number of hours studied per week in students aged 18-20 is 7 while in the age group 21-24, only 5 hours were used to study. Assuming that the standard deviation for the first group is 4.2 and the second group is 4.1, is there a significant difference in the hours studied between the two groups at a = 0.05? Assume the standard deviations are not equal to eachother.
There is not enough evidence to suggest that the number of hours studied between the two groups is different.
What is the regression line for the data below?
Student: A B C D E F G H I J K L
Mis. As: 2 0 2 1 7 8 4 6 1 0 3 4
Grade: 87 98 82 92 61 55 78 80 88 100 43 79
y' = 93.06 - 4.57x
It was found that the average American eats 23 chickens a year. Assume the variable is normally distributed and the standard deviation is 1.7. If 13 adults are randomly selected, find the probability that the mean number of chickens eaten per year is greater than 22.5.
.8554 or 85.54%
A large urgent care center with 5 doctors found that they can see an average of 21 patients per hour. Assume the population standard deviation is 4.2. A random sample of 53 hours were selected. Find the 98% confidence interval of the mean number of patients seen in a one-hour period.
(19.66, 22.34)
It was found that the average amount of student loan debt at a 4-year university is $52,330. To see if the average amount of debt has changed a researcher selects a sample of 7 universities and finds that the average debt is $47,540. The population standard deviation is $4,230. At a = 0.01, can it be concluded that the average amount of debt has changed?
There is significant evidence that the amount of debt a student is in has changed.
A teacher wishes to see if students were to study more, their grade would increase. The results are from test 1 to test 2. Can it be concluded that the test scores have increased over the two tests at a=0.01?
Subject 1 2 3 4 5
Grade 1 3 5 6 2 11
Grade 2 5 8 4 6 17
There is not enough evidence to show that the test scores have increased over the two tests.
What is the coefficient of determination?
Student: A B C D E F G H I J K L
Mis. As: 3 0 2 1 7 8 4 6 9 0 3 4
Grade: 90 98 82 92 61 60 78 80 23 100 63 79
.736
The average age of a vehicle registered in the US is 7.8 years. Assume the standard deviation is 15 months. If a random sample of 22 vehicles is selected, find the probability that the mean age of vehicles is between 7.5 and 8.1 years.
.7416 or 74.16%
A survey of 70 adults found that 52% said they would retire after age 55. Find the 95% confidence interval of the true proportion who said they would retire after age 55.
(0.40, 0.64)
Sugar is packed in 4-pound bags. Someone suspects that there is less sugar in the bags. A sample of 32 bags produced a mean of 3.8 pounds and a standard deviation of 0.6 pounds. Is there enough evidence to conclude that the bags contain less than 4 pounds? Make your decision when a = 0.05.
We have significant evidence to conclude that the weight of the sugar bags is less than 4 pounds.
A survey of 200 randomly selected male and female workers, equally male and female, found that 8% of male workers said they'd work more than 6 days while 12% of females said they'd work more than 6 fays a week. At a = 0.01, can it be concluded that the percentage of males is less than the percentage of female workers?
There is not enough evidence to conclude that the percentage of males willing to work more than 6 days a week is less than the percentage of women willing to work more than 6 days per week.
Using the data from the previous question, Chapter 10 400, test the significance of the relationship between the variables when a = 0.05.
There is a strong, negative linear relationship between a students number of missing assignments and the grade in the class.