Learning Activity Modules 5 and 6Name_______________________
Date_______________________
Please show all work or no credit will be given. Make sure you are using Microsoft Word to
open this assignment to ensure all questions are opening correctly.
1. According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample
of 300 adults is obtained.
a) Describe the sampling distribution of 𝑝̂ , the sample proportion of adults who smoke. (6 points)
b) In a random sample of 300 adults, what is the probability that at least 50 are smokers? (5 points)
c) Would it be unusual if a random sample of 300 adults results in 18% or less being smokers? Please
explain. (6 points)
2. Clayton Kershaw of the Los Angeles Dodgers is one of the premier pitchers in baseball. His most
popular pitch is a four-seam fastball. The data below represent the pitch speed (in miles per hour) for a
random sample of 18 of his four-seam fastball pitches.
Four
seam
fast
pitch
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Speed
(miles per
hour)
93.63
93.83
94.18
94.71
95.52
95.07
95.12
94.75
95.35
94.70
94.15
95.28
94.62
95.49
96.08
95.77
93.86
93.34
a) Is “pitch speed” a quantitative or a qualitative variable? (1 point)
b) Draw a boxplot and check to see if the data set has any outliers. Does the data set has any outliers? (5
points)
c) Assuming the requirements for constructing a confidence interval for the mean are satisfied,
Construct and interpret a 95% confidence interval for the mean pitch speed of a Clayton Kershaw fourseam fastball. (6 points)
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