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Institution
Chapter 11 Stats

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Uploaded on April 22, 2024
Number of pages 30
Written in 2023/2024
Type Exam (elaborations)
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chapter 11 stats
ecologists conducted a study to investigate the p
if the proportions of nests occupied is the same f

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Ecologists conducted a study to investigate the potential ecological
impact of golf courses. Investigators monitored the reproductive
success of bluebirds in birdhouses at nine golf courses and ten
similar birdhouses at nongolf sites. Data on nests in birdhouses
occupied only by bluebirds are shown in the table.
Observed Number of Nests per Birdhouse by Location
0 nests1 nest2 or 3
nestsTotalGolf3042880Nongolf405822120Total7010030200
If the proportions of nests occupied is the same for golf and nongolf
sites, what would be the expected count of birdhouses with 1 nest in
nongolf locations?
60
A fisheries biologist collected a random sample of fish from a lake
and conducted a chi-square goodness-of-fit test to see if the
distribution of fish changed over time. The table below shows the
distribution of fish that were put into the lake when it was
originally stocked.
Fish TypeTroutBassPerchSunfishCatfishPercent25%25%20%15%15%
The biologist found evidence to reject the null hypothesis in favor
of the alternative hypothesis. Which of the following represents the
alternative hypothesis of the test?
At least one of the fish proportions is different than the
corresponding proportion when the lake was originally stocked.
10 Must-Have Accessories for Sprucing Up Your Caravan
A factory produces bags of rubber bands. A bag of rubber bands has
five different sizes: extra large (XL), large (L), medium (M), small
(S), and extra small (XS). A quality control specialist collects a
random sample of 450 rubber bands from the bagging machine and
calculates a chi-square goodness-of-fit test to see if the
frequencies for each size in the sample match the hypothesized
distribution. The quality control specialist will test his sample
against the following null hypothesis
Ho:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10Ho :pXL =0.10,pL =
0.20,pM =0.40,pS =0.20,pXS =0.10
How many medium rubber bands are expected in the random sample of 450
rubber bands?
180

,At a certain company, loan agents are paid based on the number of
loans they close in a day. Based on company records, the number of
loans X that a randomly selected loan agent closes on a randomly
selected day has the probability distribution below.
x1234567P(x)0.050.100.220.300.180.120.03
At the company, the daily salary of a loan agent is $150 plus $50 per
loan closed. Let Y represent the amount of money made by a randomly
selected loan agent on a randomly selected day. Which of the
following statements is NOT true?
The mean daily salary is greater than $350 per day.
A newspaper article indicated that 43 percent of cars with black
seats are white, 46 percent of cars with black seats are blue, 7
percent of cars with black seats are red, and 4 percent of cars with
black seats are black. A test was conducted to investigate whether
the color of cars with black seats was consistent with the newspaper
article. A random sample of cars of these colors was selected, and
the value of the chi-square test statistic was χ2=8.2χ2=8.2. Which
of the following represents the p-value for the test?
P(χ2≥8.2)=0.04
Nonnative speakers of English often have characteristics in their
handwriting that differ depending on the speaker's first language.
Handwriting samples from a random sample of Chinese, Malay, and
Indian children in a school in Singapore were taken to investigate
these differences. One characteristic of interest was a rounding at
the top of the capital letter A. Data for the top-rounding
characteristic for a sample of 153 children are shown in the table.
Observed Top Rounding on the Capital Letter A
MalayIndianChineseTotalYes 921 8 38No423142115Total515250153
If children from these countries exhibit top rounding in the same
proportions, what is the expected count for Malay children who show
top rounding?
(153(38)(51) )
Let X be a random variable whose values are the number of dots that
appear on the uppermost face when a fair die is rolled. The possible
values of X are 1, 2, 3, 4, 5, and 6. The mean of X is 7/2 and the
variance of X is 35/12. Let Y be the random variable whose value is
the difference (first minus second) between the number of dots that
appear on the uppermost face for the first and second rolls of a fair
die that is rolled twice. What is the standard deviation of Y ?
3512+35121235 +1235
not just the adding one
The National Park Service writes materials for students to use while
in the parks. In a study of the effectiveness of some of these
materials, a random sample of students was selected to take a short

, quiz about oak trees after using these materials. A random sample of
park professionals also took the quiz. Investigators compared
classifications (low, medium, and high) of the crown shapes—the
general shapes of the leafy parts of the trees—made by students in s
6 through 12 with classifications made by professionals. Data from
the study are shown in the table.
ProfessionalsStudentsTotalLow544397Medium483987High7916Total10991200
If the professionals and the students do not differ in the
distributions of their responses, which of the following is equal to
the expected number of students who classify the crown shapes as
medium?
(200(87)(91) )
For which of the following is a chi-square goodness-of-fit test most
appropriate?
Determining whether a categorical variable has a significantly
different distribution of proportions than the expected distribution
A recent survey concluded that the proportion of American teenagers
who have a cell phone is 0.27. The true population proportion of
American teenagers who have a cell phone is 0.29. For samples of size
1,000 that are selected at random from this population, what are the
mean and standard deviation, respectively, for the sampling
distribution of the sample proportion of American teenagers who have
a cell phone?
0.29,1000(0.29)(0.71) the one where it's divided by 1000
Type of Grass SeedPercentFescue (F)55%Buffalo grass (B)22%Blue grama
(BG)10%Indian grass (I)7%Green needlegrass (NG)6%
A quality control specialist tests samples of the seed being packaged
and uses a chi-square goodness-of-fit test to see whether the
proportions in the samples match what is claimed by the company.
Which of the following best describes the null hypothesis and the
alternative hypothesis for the test?
Ho:pF=0.55,pB=0.22,pBG=0.10,pI=0.07,pPNG=0.06Ho :pF =0.55,pB =
0.22,pBG =0.10,pI =0.07,pPNG =0.06
Ha:Ha :At least one of the proportions is different
Each person in a random sample of adults indicated his or her
favorite color. The results, shown in the table below, are reported
by age group of the respondents.

If choice of color is independent of age group, which of the
following expressions is equal to the expected number of respondents
who are aged 30 to 50, inclusive, and prefer green?
314(99)(108)
A company claims they produce their mixed bag of candies so that, of
the candies in the bag, 20 percent are dark chocolate, 60 percent are

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