Discuss the following problems:
Q1) A toy manufacturer claims that the mean time that its top-selling toy captures children's attention is at least 35 minutes. Suppose that we doubt this claim and we carry out a hypothesis test to see if we can refute the claim. State the null hypothesis ho and the alternative hypothesis h1 that we would use for this test.
Q2) Some college grads work more than 40 hours a week, and some work fewer. We want to test if the average number of hours worked is greater than 40. The mean of a random sample is 42 and the standard deviation is 5.
What is a type I error? Suppose we decide not to reject the null hypothesis. What kind of error might we be making.
Q3) A company has a completion time with μ = 12.9 minutes, standard deviation = 1.1 minutes. It is claimed that the mean completion time has decreased. A random sample of 90 times was taken. The sample mean was 12.6.
4) Mean value for blood pressure is 120. Sample mean = 130, n = 14, and standard deviation is 21.
Q5)Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, p. is greater than 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 42 hours and that the standard deviation is 5 hours.
Based on this information, answer the questions below.
What are the null hypothesis (Ho ) and the altemathe hypothesis (Hi ) that should be used for the test?
In the context ofthis test, what is a Typat error?
Suppose that we decide not to reject the null hypothesis. What sort of error might we be mating"
Q7: Loretta, who turns 91 this year, has heard that the mean systolic blood pressure among the elderly is millimeters of mercury 120 (mmHg), but she believes that the actual value is higher. She bases her belief on a recently reported study of 22 randomly selected, elderly adults. The sample mean systolic blood pressure of the adults in the study was 130 mmHg, and the sample standard deviation was 20 mmHg.
Assume that the population of systolic blood pressures of elderly adults is normally distributed. Based on the study, at the .05 level of significance, can it be concluded that , the mean systolic blood pressure among elderly adults, is greater than 120 mmHg?
Perform a oneatedtest.lhen fininme table below.
Perform a one4ailed test. Then All inn table Debts,.
The null hypothesis
The alternate hypothesis
The type of test statistic
The value of test statistic
Q8: An automobile assembly line operation has a schedule mean completion time,or 12.9 minutes.The standard deviation of completion times is 1. minutes.It is clained under new management,the mean completion time has decreased.To test the claim,a random sample of 90 completion times under new management was taken.The sample had a mean of 12.6 ,inutes.Can we support at the 0.01 level of signifiance,the claim that the meancompletion time has decreasedunder new management?Assume the standard deviation of completion times has not changed.
Perform a one tailed test.Then fill in the table below:
Perform a one4ailed test. Then All inn table Debts,.
The null hypothesis
The alternate hypothesis
The type of test statistic
The value of test statistic
The critical at the 0.01 level of significance.