Question

Your firm has two manufacturing facilities in North Texas. Suppose that for years the mean number of units manufactured per shift for plant 1 has been accepted to be the same as the mean number of units for plant 2. However, now plant 1 is believed to have a greater (>) mean than plant 2. Letting ? = .05 and assuming the populations have equal variances and x is approximately normally distributed, conduct a hypothesis to test this belief.
What is the correct hypothesis statement?
H0: ?1 ? ?2 -or- ?1 - ?2 ? 0
HA: ?1 < ?2 -or- ?1 - ?2 < 0

H0: ?1 = ?2 -or- ?1 - ?2 = 0
HA: ?1 ? ?2 -or- ?1 - ?2 ? 0

H0: ?1 ? ?2 -or- ?1 - ?2 ? 0
HA: ?1 > ?2 -or- ?1 - ?2 > 0

H0: ?1 ? ?2 -or- ?1 - ?2 ? 10
HA: ?1 < ?2 -or- ?1 - ?2 < 10

Your firm has two manufacturing facilities in North Texas. Suppose that for years the mean number of units manufactured per shift for plant 1 has been accepted to be the same as the mean number of units for plant 2. However, now plant 1 is believed to have a greater mean than plant 2. Letting ? = .05 and assuming the populations have equal variances and x is approximately normally distributed, conduct a hypothesis to test this belief. Data consists of 10 samples from each plant.
What is the critical value?
Round to three digits and include leading zeros if necessary.
What is the decision rule?
If the calculated test statistic is less than -1.734, reject the null hypothesis.
If the calculated test statistic is less than -2.101, reject the null hypothesis.
If the calculated test statistic is greater than 1.734, reject the null hypothesis.
If the absolute value of the calculated test statistic is greater than 1.734, reject the null hypothesis.

What is the calculated value of the test statistic?
Round to three digits and use leading zeros if necessary.
What is your decision about the null hypothesis?

Fail to reject.
Reject.
Conclude the null is supported.
Find the null is true.
Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentine’s Day. Suppose a researcher wants to test this hypothesis by randomly sampling nine men (sample1) and 10 women (sample 2) with comparable demographic characteristics from various large cities across the United States. Each study participant is asked to keep a log beginning one month before Valentine’s Day and record all purchases made for Valentine’s Day during that one-month period. . Use a 1% level of significance to test to determine if, on average, men actually do spend significantly more than women on Valentine’s Day. Assume that such spending is normally distributed in the population and that the population variances are equal.
What is the correct hypothesis statement?
H0: ?1 ? ?2 -or- ?1 - ?2 ? 0
HA: ?1 < ?2 -or- ?1 - ?2 < 0

H0: ?1 = ?2 -or- ?1 - ?2 = 0
HA: ?1 ? ?2 -or- ?1 - ?2 ? 0

H0: ?1 ? ?2 -or- ?1 - ?2 ? 0
HA: ?1 > ?2 -or- ?1 - ?2 > 0

H0: ?1 ? ?2 -or- ?1 - ?2 ? 10
HA: ?1 < ?2 -or- ?1 - ?2 < 10

What is the absolute value of the critical value?

What is the decision rule?
If the calculated test statistic is greater than -2.567, reject the null hypothesis.
If the calculated test statistic is greater than 2.567, reject the null hypothesis.
If the absolute value of the calculated test statistic is greater than 2.567, reject the null hypothesis.
If the absolute value of the calculated test statistic is less than -2.567, reject the null hypothesis.

Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentine’s Day. Suppose a researcher wants to test this hypothesis by randomly sampling nine men (sample1) and 10 women (sample 2) with comparable demographic characteristics from various large cities across the United States. Each study participant is asked to keep a log beginning one month before Valentine’s Day and record all purchases made for Valentine’s Day during that one-month period. . Use a 1% level of significance to test to determine if, on average, men actually do spend significantly more than women on Valentine’s Day. Assume that such spending is normally distributed in the population and that the population variances are equal. Data are in the attached file below.

Men	Women
$ 107.48	$ 125.98
$ 43.61	$    45.53
$ 90.19	$    56.35
$ 125.53	$    80.62
$ 70.79	$    46.37
$ 83.00	$    44.34
$ 129.63	$    75.21
$ 154.22	$    68.48
$ 93.80	$    85.84
	$ 126.11

What is the calculated value of the test statistic?
Round to three digits and use leading zeros if necessary.

What is your decision about the null hypothesis?
Fail to reject.
Reject.
Conclude the null is supported.
Find the null is true.

Using Excel determine the exact p-value.
Round to four digits and use leading zeros if necessary.

Answer 1