Transcript Hypothesis Tests with Critical Values

Hypothesis Tests
with Critical Values
Critical Value:
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Based on the alpha level. Use the z or t
chart and look it up. This goes on the
graph.

Reject the Ho if the observed test statistic
is bigger than the absolute value of the
critical test value.
The mean score on a standardized test is 1100 with a standard
deviation of 100 points. We sampled a group of 50 honor students and
found their mean was 1150. Do the honor students score higher on this
test. Use a 5% level of significance.
A travel association claims that the mean daily meal cost for two adults
traveling together on vacation in San Francisco is $105. A random
sample of 20 such groups of adults has a mean daily meal cost of $110
and a standard deviation of $8.50. Is there enough evidence to reject
the claim at  = 0.01?
The mean ACT scores for 43 male high school students is 21.1 and the
standard deviation is 5.0. The mean ACT score for 56 female high
school students is 20.9 with a standard deviation of 4.7. At  = 0.01,
can you reject the claim that male and female high school students
have equal ACT scores?
On a tv show, eight contestants try to lose the highest percentage of
weight in order to win a cash prize. The table shows the times (sec) of
the contestants at the beginnings of the season and at the end of the
season. At  = 0.01, is there enough evidence to conclude that the
contestants’ times have improved?
Cont
1
2
3
4
5
6
7
8
Beg
130.2
104.8
100.1
136.4
125.9
122.6
150.4
158.2
End
121.5
100.7
90.2
135
112.1
120.5
139.8
142.9
A medical researcher claims that 5% of children under 18 years of age
have asthma. In a random sample of 250 children under 18 years of
age, 9.6% say they have asthma. At  = 0.10, is there enough
evidence to support the center’s claim?
In a survey of 600 motorcyclists, 404 wear a helmet. In another survey
of 500 motorcyclists taken one year before, 317 wore a helmet. At  =
0.05, can you support the claim that the proportion of motorcyclists who
wear a helmet is now greater?
A doctor believes that the number of births by day of the week is
uniformly distributed. Test using a 5% level of significance.
Day
Freq
Sun
65
Mon
103
Tues
114
Wed
116
Thur
115
Fri
112
Sat
74
Homework
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Worksheet