Statistics-Identify the null hypothesis and the alternative hypothesis

1.
Consumption of large amounts of
alcohol is known to increase reaction time. To investigate the effects of small
amounts of alcohol, reaction time was recorded for five individuals before and
after the consumption of 2 ounces of alcohol.
Do the data below suggest that consumption of 2 ounces of alcohol
increases mean reaction time?

	Reaction Time (seconds)
Subject	Before After
1	6 7
2	8 8
3	4 6
4	7 9
5	9 8

Assume we
want to use a 0.05 significance level to test the claim.

(a)Identify
the null hypothesis and the alternative hypothesis.

(b)
Determine the test statistic. Show all work; writing the correct test
statistic, without supporting work, will receive no credit.

(c)
Determine the P-value. Show all work; writing the correct P-value, without supporting work,
will receive no credit.

(d)
Is there sufficient evidence to
support the claim that consumption of 2 ounces of alcohol increases mean
reaction time? Justify your conclusion.

3. The MiniMart sells five
different types of coffee mugs. The manager reports that the five types are
equally popular. Suppose that a sample of 500 purchases yields observed counts
120, 90, 110, 100, and 80 for types 1, 2, 3, 4, and 5, respectively.

Type	1	2	3	4	5
Number of Mugs	120	90	110	100	80

Assume
we want to use a 0.05 significance level to test the claim that the five types
are equally popular.

(a)
Identify the null hypothesis
and the alternative hypothesis.

(b)
Determine the test statistic. Show all work; writing the correct test
statistic, without supporting work, will receive no credit.

(c)
Determine the P-value for the test. Show all work; writing the correct P-value,
without supporting work, will receive no credit.

(d)
Is there sufficient evidence to
support the manager’s claim that the four types are equally popular? Justify
your answer.

4. A
random sample of 4 professional athletes produced the following data where x is
the number of endorsements the player has and y is the amount of money made (in
millions of dollars).

x	0	1	3	5
y	1	2	5	8

(a)
Find an equation of the least
squares regression line. Show all work; writing the correct equation,
without supporting work, will receive no credit.

(b)
Based on the equation from part
(a), what is the predicted value of y
if x = 4? Show
all

work and justify your
answer.