Math 115 Ch 8 pt 1.2 CW, Greg O'Brien (2)
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Apr 3, 2024
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Math 115 Ch 8 pt 1.2 CW
Name:
Greg O’Brien
11/5/23
1.
Harper’s Index
claims that 23% of people in the U.S. are in favor of outlawing cigarettes. You decide to test this
claim and ask a random sample of 200 people in the U.S. whether they are in favor of outlawing cigarettes. Of the
200 people, 54 are in favor of outlawing cigarettes.
a)
Write the claim using plain language and then write it using mathematical symbols.
The claim is that 23% of people in the U.S. in the U.S. are in favor of outlawing cigarettes.
b)
Write the Null Hypothesis H
0
and the Alternative Hypothesis H
1
using mathematical symbols. Label the claim and
the tail-type.
H
0
:
Claim: p = 0.23 two-tailed
(p is proportion)
H
1
:
p
≠
0.23 two-tailed
(p is proportion)
c)
Label all the values in the prompt that are not mentioned in the claim with an appropriate variable.
n = 200
x = 54
2.
In a random sample of 26 computers, the mean repair cost was $150 with a standard deviation of $36. Assume
the cost of computer repairs is normally distributed. CNET claims that the average computer repair cost is $100.
a)
Write the claim using plain language and then write it using mathematical symbols.
The claim is that the average computer repair cost is $100.
b)
Write the Null Hypothesis H
0
and the Alternative Hypothesis H
1
using mathematical symbols. Label the claim and
the tail-type.
H
0
:
Claim: μ = $100 two-tailed
H
1
:
μ
≠
$100 two-tailed
c)
Label all the values in the prompt that are not mentioned in the claim with an appropriate variable.
n = 26
x
(with line above, population mean)
= $150
s = $36
d)
We constructed, with a significance level of μ
= .05
, a confidence interval for the mean of the form
$135.46 <
μ
< $164.54
Make a decision about the null hypothesis H
0
and interpret that decision in the context of the problem.
With a significance level of 0.05, CNET’s claim of $100 being the average computer repair cost is not
within the μ and the true average computer repair cost is most likely between the price of $135.46 and $164.54.
With this data, we can reject the null hypothesis/CNET’s claim.
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