# Hypothesis Testing

See the attachments for the complete descriptions of the questions.

1.) 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.

2.) 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.

3.) 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.

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#### Solution Preview

1.) 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.

The null hypothesis is H0: μ ≥ 35, and the alternate hypothesis is Ha: μ < 35; where μ is the mean number of minutes the toy holds a child's attention. Because we're testing that the mean is less than 35 (rather than not equal to 35), we would use a one-sided test (probably a t-test).

2.) Some ...

One and Two Tailed Tests: Hypothesis Testing Problem

Ho: u = 50

H1: u not = 50

The sample mean is 49, and the sample size is 36. the population standard deviation is 5. Use the .05 significance level.

a. Is this a one or two tailed test.

b. What is the decision rule?

c. What is the value of the test statistic?

d. What is your decision regarding Ho?

e. What is the p-value? Interpret it.