## Transcribed Text

1. (Hypothesis Testing) Coin flip: Let p be the probability of showing heads in one flip
experiment. We wish to test Ho p = 0.5, against Ha p> 0.5. The test statistic 0 is
Y the number of heads observed. Let's do 50 experiments and we observed Y = 30.
Use a test level 0.05 to make a conclusion if the data provide sufficient evidence to
support our research hypothesis Ha.
2. (Large-Sample Tests) Shear strength measurements derived from unconfined com-
pression tests for two types of soils gave the results shown in the following table
(measurements in tons per square foot), where or and T2 represent the standard de-
viation of measured data. Do the soils appear to differ with respect to average shear
strength, at the 1% significance level?
Soil #1
Soil #2
721 35
n.2 40
y1 1.68
y/2 1.45
o1 0.26
T2 0.23
3. (Compute Type II Error) We have two different cakes (red and blue), and we want
to check the weight of fat in them. Independent random samples of 55 red cakes and
55 blue cakes were collected, as shown in the table. Testing hypotheses: Ho 0 =
11 - 12 = Oo against Ha 0 = 11 - 12 > 0o.
Red
Blue
72.1 55
112 55
P1 = 4.0 g
12 3.8 g
of = 0.36
a: 0.24
(a) Choose correct Oo and answer: do the red cakes contain more fat than the blue
cakes, at the 5% significance level?
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(b) Given a = 0.05, Oo = 0 and OF = 0.3. what's the probability of Type II error?
(c) Given a = 0.05, B = 0.05, 00 = 0 and 0. = 0.3, find the sample size for the
upper-tailed test.
4. (p-values) A pharmaceutical company conducted an experiment to compare the mean
times (in days) necessary to recover from the effects and complications that follow the
onset of the common cold. This experiment compared persons on a daily dose of 500
milligrams (mg) of vitamin C to those who were not given a vitamin supplement. For
each treatment category, 55 adults were randomly selected, and the mean recovery
times and standard deviations for the two groups were found to be as given in the
accompanying table.
Treatment
No supplement
500mg Vitamin C
72.1 55
72.2 55
M 6.5
M2 5.8
01 2.9
o2 1.2
(a) Do the data indicate that the use of vitamin C reduces the mean time required to
recover? Find the attained significance level.
(b)What would the company conclude at the a = 0.05 level?
5. (Small Sample Tests) The price of a popular sneaker at a national chain store is $52.
Jack bought six of the same sneaker at an online auction site for the following prices:
Price: $44 $46 $49 $58 $43 $38
Assuming that the auction prices of sneakers are normally distributed, determine
whether there is sufficient evidence in the sample, at the 5% level of significance, to
conclude that the average price of the sneaker is less than $52 if purchased at an online
auction.
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