Econ E370 HW 8
A tire manufacturer has been producing tires with an average life expectancy of 25,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 24 25 Calculate the p-value for the test
0.079
Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 120 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.1. Calculate the p-value for the test
0
In a one-tailed hypothesis test (lower tail), the t test statistic is determined to be -2.75. The sample size is 45. The p-value for this test is
0.0043
Which of the following statements is correct?
We cannot establish a claim if the null hypothesis is not rejected
If a hypothesis is rejected at 5% level of significance, it (Hint: draw a picture for this question)
may be rejected or not rejected at the 1% level
In a two-tailed hypothesis test, the t test statistic is determined to be -2.7. The degrees of freedom for the test is equal 15. The p-value for this test is
0.0165
In a two-tailed hypothesis test, the t test statistic is determined to be 2.45. The sample size is 25. The p-value for this test is
0.022
In a one-tailed hypothesis test (upper tail), the t test statistic is determined to be 1.95. The sample size is 25. The p-value for this test is
0.0315
Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 500 employees, 230 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Calculate the critical value for the test
-1.6449
For a one-tailed test and a sample size of 25 observations at 5% significance level, the critical value of t is (Hint: you are given the sample size, not the degrees of freedom)
-1.7109
Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 500 employees, 230 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Compute the test statistic
-1.7889
Consider the following hypothesis test: H0:u≥42; H1:u<42 A sample of 49 observations provides a sample mean of 38 and a sample standard deviation of 7. Compute the value of the test statistic.
-4
Representatives of a large national union announced that the fraction of women in the union was equal to one-half in the previous year. You are interested in testing whether there has been a change in the fraction of women this year. How would you set up the hypothesis test?
H0: p = 0.5; H1: ≠ 0.5
Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 120 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.1. Provide the null and the alternative hypotheses
H0: p≤0.21: H1 > 0.21
The National Association of Realtors reported that 28% of home buyers in the state of Florida were foreigners in 2019. In 2021, a group of students from Indiana University conducted a study and, based on a sample of 100 people, concluded that 30% of home buyers in the state of Florida are foreigners. So, the members of the group think that the proportion has increased since then. The correct hypothesis statement for the student's group to test is
H0: p≤0.28; H1: p>0.28
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighted to determine whether overfilling or under filling is occurring. If the sample data led to a conclusion of under filling or overfilling, the production line would be shut down and adjusted to obtain a proper filling. The correct hypothesis statement for this test would be
H0: u = 32; H1: ≠ 32
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.2 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is any different from 3 minutes (use the significance level 0.05 for the test). Provide the null and the alternative hypotheses.
H0: u = 3; H1: u≠3
A tire manufacturer has been producing tires with an average life expectancy of 25,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 24 25 Provide the null and alternative hypotheses
H0: u ≤ 25; H1 u > 25
Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 500 employees, 230 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Provide the null and the alternative hypotheses.
H0: u≥0.5; H1: u < 0.5
Think about the hypothesis test: H0:u≥42; H1:u<42 A sample of 49 observations provides a sample mean of 38 and a sample standard deviation of 7. The null hypothesis will be rejected if
t x bar < -ta
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.2 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is any different from 3 minutes (use the significance level 0.05 for the test). State your conclusion for the test
t x bar > t a/2 => we reject Ho. Therefore, there is enough evidence to conclude that the mean waiting time of all customers is different from 3 minutes.
In the past, the average age of employees of a large corporation has been 50 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 55 years with a standard deviation of 16 years.The company would like to set a=0.05 for the hypothesis test. It is known that za=1.645 and ta=1.669 for the df = 63. The conclusion for this hypothesis test would be
t x bar > ta . So, we reject the null and can conclude that there has been an increase in the average age of the employees in the corporation.
Breyers is a major producer of ice cream and would like to test if the average American consumes more than 17 ounces of ice cream per month. A random sample of 25 Americans was found to consume an average of 20 ounces of ice cream last month. The standard deviation for this sample was 5 ounces.Breyers would like to set a=0.025 for the hypothesis test. It is known that za=1.96 and za=2.06 for the df = 24. Also, it is established that the ice cream consumption follows the normal distribution in the population. The conclusion for this hypothesis test would be
t x bar > ta. So, we reject the null and can conclude that the average amount of ice cream consumed per month is greater than 17 ounces.
The Department of Economic and Community Development (DECD) reported that in 2009 the average number of new jobs created per county was 450 (the only information that you know from DECD). Doing a project in your international economics class, you want to determine whether there has been a decrease in the average number of jobs created, and you collect information about 11 countries.To conduct the hypothesis test, what distribution would you use to calculate the critical value and the p-value?
the Student's t-distribution with 10 degrees of freedom
The level of significance is the
the probability of a type I error
Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person.To conduct the hypothesis test, what distribution would you use to calculate the critical value and the p-value?
the standard normal distribution
When conducting a hypothesis test for the population mean when σ is unknown and the sample size is 30 or more, the distribution we use for computing the critical value and the p-value is
the student's t-distribution
A tire manufacturer has been producing tires with an average life expectancy of 25,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 24 25 Compute the test statistic
1.6592
For a two-tailed test and a sample of 15 observations at 10% significance level, the critical value of t is (Hint: you are given the sample size, not the degrees of freedom)
1.7613
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.2 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is any different from 3 minutes (use the significance level 0.05 for the test). Calculate the critical value for the test
1.9842
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.2 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is any different from 3 minutes (use the significance level 0.05 for the test). Compute the test statistic
4
Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 120 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.1. Compute the test statistic
4.4193
Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 500 employees, 230 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Suppose that, instead of the critical value approach, you decided to use the p-value approach and found that the p-value for the test in this problem is equal to 0.0368. This p-value is best interpreted as the following:
If the true proportion of female employees in the company was 50%, then there would be a 3.68% chance of observing a proportion of females equal to or below 46% in the sample of 500 individuals.
Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 120 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.1. The p-value is best interpreted as the following:
The p-value indicates the probability of observing the proportion of people who like new flavor equal to 30% or greater in the sample of 400 individuals, if actual proportion of people who like the new flavor is 21%.
A tire manufacturer has been producing tires with an average life expectancy of 25,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 24 25 Do we need any additional assumptions about the life expectancy of the tires in the population to make sure that the conclusion stated in the previous question is reliable?
Yes. The life expectancy of the tires should follow the normal distribution in the population which would guarantee that the conclusions derived in the test are reliable.
Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 120 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.1. State your conclusion for the test using the p-value.
p-value < 0.05, so we reject Ho. Therefore, there is enough evidence to conclude that the proportion of people who like new favor is above 21%.
A tire manufacturer has been producing tires with an average life expectancy of 25,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 24 25 State your conclusion using the p-value and the significance level of 3%.
p-value > 0.03, so we do not reject Ho. Therefore, there is not enough evidence to conclude that the mean life expectancy of the new tires has increased.
Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 500 employees, 230 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). State your conclusion for the test using the critical value
zp < -za => so, we reject Ho. Therefore, there is enough evidence to conclude that there has been a reduction in the percentage of females in the company.
