finds my work suspicious of cheating

Miss Y, SPR 2020
STAT 10, Final Exam Name:
Read each question carefully and show all work.
Full credit will only be given if all correct work/steps are shown.

The following must be read and signed for the exam to be considered and counted in final grade.
I acknowledge that the following exam is entirely of my own work. Also, I acknowledge that
if Miss Y. finds my work suspicious of cheating, there may be consequences of failing this
exam or being reported to the Office of Student Conduct and Integrity.
Signature:
1. (11 points) Match each term/symbol with its definition or use.
Variable µ Quantitative σ Relative Frequency ¯ x
Z-score s Dispersion IQR Range
· This is how data is spread:
· This is a unitless value that is the distance from the mean in terms of standard deviations:
· This represents the population standard deviation:
· This is the distance from the highest and lowest data value:
· This represents the sample mean:
· This represents 50% of the data that is centered about the median:
· This is the characteristics of the individuals in a population that can be measured or categorized:
· This is the proportion of observations within a category:
· This represents the population mean:
· This describes the variables that are numerical:
· This represents the sample standard deviation:
2. (6 points) Identify what type of correlation the following data sets have. Draw a line from the
correct correlation to its matching data set.
· Positive Correlation
· Negative Correlation
· No Correlation
· The age of a car and the value of a car.
· The age of a house and the number of people
living in a house.
· The number of hours driven and the number
of miles driven.
3. (4 points) It was thought, the average time to order and deliver a pizza at Nino’s pizza was
48 minutes. Nino, the owner, believes a new system will reduce the time. With this, we get
the following null and alternate hypotheses:
H0: µ = 48
H1: µ < 48
Explain what it would mean for Nino to make a type II error. Describe in terms of this problem,
do not use generic words.
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4. (13 points) The following data represents just some of the flight times (in minutes) from Los
Angeles to Cincinatti:
282 270 260 266 257 260 267
Calculate the standard deviation (there were two methods, and I want you to choose whichever
is best for yourself). Draw a chart if you feel you need to, but I want to see all work shown.
Round to two decimal places. [Hint: sample or population]
5. (6 points) A by-hand car wash owner wants to hire more employees and is interested in
consistent results and time. He times (follows a normal distribution) the applicants in washing
a car and find the that the mean is 14:8 minutes with a standard deviation of 3:1 minutes.
What proportion of wash times will be greater than 21 minutes?
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6. (5 points) The time it takes for a batch of tapioca balls to cook is normally distributed with
µ = 13 minutes and σ = 2:5 minutes. Consider a sample of 9 different batches of tapioca balls.
Find the probability that the mean cook time is less than 10:7 minutes.
7. (11 points) Fill in the missing columns for the following frequency distribution that shows the
HDL cholesterol levels for all 20-30 year old patients of one physician (use :
a)

b) Draw and clearly label a frequency histogram for this data.
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8. (18 points) On any given day, Otis Campbell has a 31% chance of walking into the Mayberry
jail uninvited. Suppose we randomly choose 15 days to observe if Otis walks into the jail or
not.
a) Check that this is a binomial probability (4 checkpoints to meet).
b) What is the probability that Otis shows up exactly 3 days? Round to three decimals.
c) What is the probability that Otis shows up one or more days? Round to three decimals.
[Hint: there is a shortcut to calculating this]
e)
µ = 7:75 and σ = 2:31. Find the usual range. Write as an interval.
f) Is it usual for Otis to show up to the Mayberry jail 10 days out of 15, uninvited? Why?
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9. (17 points) The following data shows the number of times within a year Lucy Ricardo tried
to get into one of her husband’s shows. Assume that her attempts are normally distributed
and the standard deviation is s = 10:00 attempts. Construct and interpret a 95% confidence
interval for the population standard deviation of the number of attempts to get into a show.
52 30 44 35 39 26
47 37 56 26 39 28
a) Identify the degrees of freedom, n – 1.
b) Draw a Chi-Square Distribution with the critical values and areas labeled. State the two
critical values with sub-notation.
c) Find the confidence interval for the population variance. Round to two decimal places.
d) Find the confidence interval for the population standard deviation. Round to two
decimal places.
e) Interpret the results for the standard deviation confidence interval.
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10. (20 points) Archaeologist have found that the mean length of arrowheads found in New Mexico
is µ = 2:6cm. In a recent discovery in the state, archaeologist found that a sample of 61
arrowheads, gave a sample mean of 2.92cm and a sample standard deviation of 0.85cm.
Do these data indicate that the mean length of projectile points in the state is longer than
2.6cm? Use α = 0:01.
a) Establish the null and alternate hypothesis. What “tail” does this test have?
b) What is the value of the test statistic? Draw the t-value on a normal curve.
c) Find the P-value.
d) Do you reject or not reject H0? Explain.
e) Interpret the results in the context of this problem.
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11. (24 points) A random sample of potential voters were randomly divided into two groups.
Group 1: 500 potential voters (no registration reminders sent); 248 registered to vote
Group 2: 600 potential voters (registration reminders sent); 332 registered to vote
Do these data support the claim that the proportion of voters who registered was greater in
the group that got reminders. Use a 1% level of significance.
a) Find ^ p1, ^ p2, ^ p, and ^ q. Round to three decimal places.
b) State the null and alternate hypotheses.
c) What is α?
d) Calculate the test statistic, z0. Round to two decimal places.
e) Find the P-Value.
f) Do you accept or reject H0? Show.
g) Interpret the results in the context of this problem.
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