# Mathematics

Question 1 of 20

In a one-tailed hypothesis test, a critical point is a point that divides the area under the sampling distribution of a:

A. statistic into one rejection region and one nonrejection region.

B. parameter into one rejection region and one nonrejection region.

C. statistic into one rejection region and two nonrejection regions.

D. parameter into two rejection regions and one nonrejection region.

Question 2 of 20

A two-tailed hypothesis test contains

A. one rejection region and two nonrejection regions.

B. two rejection regions and one nonrejection region.

C. two rejection regions and two nonrejection regions.

D. one rejection region and one nonrejection region.

Question 3 of 20

A researcher wants to test if the mean price of houses in an area is greater than $145,000. The alternative hypothesis for this example will be that the population mean is

A. equal to $145,000.

B. not equal to $145,000.

C. greater than or equal to $145,000.

D. greater than $145,000.

Question 4 of 20

A researcher wants to test if the mean price of houses in an area is greater than $175,000. The null hypothesis for this example will be that the population mean is

A. less than or equal to $175,000.

B. not equal to $175,000.

C. greater than or equal to $175,000.

D. greater than $175,000.

Question 5 of 20

For a one-tailed test, the p-value is

A. the area under the curve between the mean and the observed value of the sample statistic.

B. twice the area under the curve between the mean and the observed value of the sample statistic.

C. the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis.

D. twice the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis.

Question 6 of 20

A two-tailed hypothesis test using the normal distribution reveals that the area under the sampling distribution curve of the mean and located to the right of the sample mean equals .028. What is the p-value for this test?

A. .028

B. .056

C. .014

D. .610

Question 7 of 20

In a hypothesis test with hypotheses H0: Mu GE 37and H1: Mu < 37 , a random sample of 54 elements selected from the population produced a mean of 35.8. Assuming that population standard deviation is 8.9 , what is the approximate p-value for this test?

A. .8389

B. .4195

C. .1611

D. .3222

Question 8 of 20

In a hypothesis test with hypotheses Ho: Mu GE 136 and H1: Mu < 136, a random sample of 67 elements selected from the population produced a mean of 130.7. Assume that population sd is 19.2 , and that the test is to be made at the 2% significance level.

What is the value of the test statistic, z?

A. 2.26

B. −1.84

C. 1.52

D. −2.26

Question 9 of 20

A researcher wants to test if the mean price of houses in an area is greater than $145,000. A random sample of 36 houses selected from the area produces a mean price of $149,100. Assume that and that the test is to be made at the 2% significance level.

What is the value of the test statistic, z?

A. −2.10

B. 1.26

C. 2.10

D. −1.26

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