# ,MATHEMATICS

Question 10 of 20

A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework. A random sample of 61 children from the school shows that they spend an average of 25.9 minutes per day on homework. Assume that minutes, and that the test is to be made at the 1% significance level.

Should you reject or fail to reject the null hypothesis in this test?

A. Reject

B. Fail to reject

Question 11 of 20

In a hypothesis test with hypotheses Ho: Mu LE 54 and H1: Mu > 54, a random sample of 24 elements selected from the population produced a mean of 59.5 and a standard deviation of 14.3. The test is to be made at the 2.5% significance level. Assume the population is normally distributed.

What is the critical value of t?

A. −2.093

B. 2.500

C. 2.064

D. 2.069

Question 12 of 20

In a hypothesis test with hypotheses Ho: Mu LE 54 and H1: Mu >54, a random sample of 24 elements selected from the population produced a mean of 59.5 and a standard deviation of 14.3. The test is to be made at the 2.5% significance level. Assume the population is normally distributed.

What is the value of the test statistic, t?

A. 1.88

B. −1.88

C. 2.92

D. 1.46

Question 13 of 20

In a hypothesis test with hypotheses Ho: Mu GE 74 and H1: Mu < 74, a random sample of 20 elements selected from the population produced a mean of 69.0 and a standard deviation of 13.7. The significance level is 1%. Assume the population is normally distributed.

What is the critical value of t?

A. −2.528

B. −1.328

C. −2.539

D. 3.733

Question 14 of 20

In a hypothesis test with hypotheses Ho: Mu GE 74 and H1: Mu < 74, a random sample of 20 elements selected from the population produced a mean of 69.0 and a standard deviation of 13.7. The significance level is 1%. Assume the population is normally distributed.

Should you reject or fail to reject the null hypothesis in this test?

A. Reject

B. Fail to reject

Question 15 of 20

A company that manufactures light bulbs claims that its light bulbs last an average of 1150 hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1094 hours and a standard deviation of 174 hours. A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1150 hours. The significance level is 5%. Assume the population is normally distributed.

What is the critical value of t?

A. −1.708

B. −1.711

C. −2.797

D. −2.787

Question 16 of 20

A company that manufactures light bulbs claims that its light bulbs last an average of 1150 hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1094 hours and a standard deviation of 174 hours. A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1150 hours. The significance level is 5%. Assume the population is normally distributed.

Does the data provide evidence to contradict the company’s claim about the average lifetime of their light bulbs?

A. Yes

B. No Reset Selection

Question 17 of 20

In a hypothesis test with hypotheses Ho: p LE .39 and H1: p > .39, a random sample of size 471 produced a sample proportion of .4475. The test is to be made at the 1% significance level.

What is the critical value of z?

A. 2.05

B. 2.33

C. 1.96

D. 2.58

Question 18 of 20

In a hypothesis test with hypotheses Ho: p GE .76 and H1: p < .76, a random sample of size 953 produced a sample proportion of .7530. The test is to be made at the 5% significance level.

Should you reject or fail to reject the null hypothesis in this test?

A. Reject

B. Fail to reject

Question 19 of 20

In a hypothesis test with hypotheses Ho: p GE .31 and H1: p < .31, a random sample of size 538 produced a sample proportion of .2855. The test is to be made at the 1% significance level.

What is the value of the test statistic, z?

A. 1.23

B. 1.15

C. −1.15

D. −1.23

Question 20 of 20

Which of the following statements describes a Type II error in hypothesis testing?

A. A court declares a defendant guilty, when he is actually innocent.

B. A scientist, trying to support a theory about the number of different species of animals in a particular country, declares the null hypothesis to be “there are 715 different species” when there are actually more than 800.

C. A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4.

D. Through hypothesis testing, we find the alternative hypothesis to be true when it is