# Mathematics

Question 1

An alternative hypothesis is an assertion that holds if the null hypothesis is false.

True

False

Question 2

If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level.

True

False

Question 3

In a given hypothesis test, the null hypothesis can be rejected at the .10 and .05 level of significance, but cannot be rejected at the .01 level.  The most accurate statement about the p-value for this test is

p-value = 0.01

p-value = 0.10

0.01 < p-value < 0.05

0.05 < p-value < 0.1

Question 4

The p-value of a test is the smallest significant level at which the null hypothesis can be rejected.

True

False

Question 5

The t-statistic is used in hypothesis testing for a mean when the actual population standard deviation is not known.

True

False

Question 6

The larger the p-value, the more we doubt the null-hypothesis.

True

False

Question 7

Alpha (α) is the probability that the sample statistic would assume a value as or more extreme than the observed value of the test.

True

False

Question 8

The null hypothesis is not rejected unless there is sufficient sample evidence to do so.

True

False

4. Individuals filing federal income tax returns prior to March 31 had an average refund of \$1102. Consider the population of “last-minute” filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15).

a.  A researcher suggests that one of the reasons that individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

b. For a sample of 600 individuals who filed a return between April 10 and April 15, the sample mean refund was \$1050 and the standard deviation was \$500. Compute the p-value.

c.  Using α =.05, what is your conclusion?

5.  The Heldrich Center for Workforce Department found that 45% of Internet users received more than 10 email messages per day. Recently, a similar study on the use of email was reported. The purpose of the study was to see whether the use of email increased.

a.  Formulate the null and alterative hypotheses to determine whether an increase occurred in the proportion of Internet users receiving more than 10 email messages per day.

b. If a sample of 420 Internet users found 208 receiving more than 10 email messages per day, what is the p-value?

c.    Using α =.05, what is your conclusion?

6.  Media Metrix, Inc. tracks Internet users in seven countries:  Australia, Great Britain, Canada, France, Germany, Japan, and the United State. According to resent measurement figures, American home users rank first in Internet usage with a mean of 14 hours per month. Assume that in a following-up study involving a sample of 205 Canadian Internet users, the sample mean was 12.8 hour per month and the sample standard deviation was 6.2 hours.

a.  Formulate the null and alterative hypotheses that can be used to determine whether the sample data support the conclusion that Canadian Internet users have a population mean less than the U.S. mean of 14 hours per month.

b.   What is the p-value?

c.   Using α =.01, what is your conclusion?

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