Download Page 1 The format on this practice exam will be similar to the format

The format on this practice exam will be similar to the format on the actual test on Tuesday, where there will be 5 show
your work problems (70 points) and then 6 multiple choice problems (30 points) for a grand total of 100 points. On the
exam, the show your work problems will have more space for you to work the problems out. Also, when showing your
work, you must use the correct mathematical notation (similar to what was used in class) as well as showing any
formulas or calculator functions that you used to solve each problem. Round each answer to 3 decimal places unless the
problem says otherwise.
1) Coca-Cola produces millions of cans of coke each year. The amount of cola in each can is from a normal distribution.
The average can of Coca-Cola has a mean of 12 oz. with a standard deviation of 0.2 oz.
a) What is the probability of getting a can that has between 11.73 and 12.27 ounces?
b) When purchasing 36 randomly selected cans of Coca-Cola, calculate 𝜇𝑥̅ 𝑎𝑛𝑑 𝜎𝑥̅ (rounded to 3 decimal places).
c) When purchasing 36 randomly selected cans of Coca-Cola, what is the probability that the mean amount of cola
will be between 11.73 and 12.27 ounces?
2) McDonald’s recently held its Monopoly Sweepstakes where people could win up to $1,000,000. McDonald’s
claimed that for each meal there’s approximately a 1 in 4 chance of winning a prize. The Hamburglar randomly
steals 91 meals that contained monopoly pieces (assume each meal had the same number of pieces). The
Hamburglar then looked at all of the pieces and noticed that 23% of those meals contained winning pieces. Suppose
we want to construct a 90% confidence interval for the proportion of winning a prize for this sweepstakes.
a) Calculate the margin of error.
b) Construct a 90% confidence interval for the proportion of winning a prize.
c) Does it seem like McDonald’s claim of 25% seem accurate? Why or why not?
3) A high school class of 20 students recently took the SAT exam. The average exam score for the class was 1583 with a
standard deviation of 298. The SAT exam scores come from a normally distributed population. We want to
construct a 99% confidence interval of the mean SAT exam scores.
a) Find the appropriate critical value for the 99% confidence interval.
𝑠
b) Use the formula 𝐸 = 𝑡𝛼/2 ∙
to calculate the margin of error.
√𝑛
c) Use your answer from part b to calculate the 99% confidence interval.
4) Mars, Inc. claims that 24% of its M&M plain candies are blue. Suppose you wanted to test this theory by collecting a
simple random sample of 50 M&M’s. You found that 17 of your 50 M&M’s are blue. Conduct a hypothesis test for
the claim that more than 24% of the M&M plain candies are blue at the 0.01 significance level. Be sure to include
the null and alternative hypothesis, test statistic, p-value or critical value (choose one), whether you reject or fail to
reject the null hypothesis, and your conclusion about the claim (whether or not you have enough evidence to
support the claim).
5) Human body temperatures were commonly believed to be an average of 98.6℉. Suppose you have a simple
random sample of 80 human body temperatures with a sample mean of 𝑥̅ = 98.2℉ and a standard deviation of
𝑠 = 0.62℉. Based on your sample, you claim that the average human body temperature should be below 98.6℉.
Use a 0.10 significance level to answer the following
a) Use the formula 𝑡
=
𝑥̅ −𝜇𝑥̅
(
𝑠
)
√𝑛
to calculate the test statistic.
b) Use your answer for part a.) to determine the p-value.
c) Calculate the appropriate critical value.
Multiple Choice
6) Many video games use rng (random number generators) to determine what happens in different situations. For
example, if the rng value was 0.65 or higher, the enemy would attack the player. If it was less than 0.65, the
enemy would try and run away. Suppose this specific rng value could be from 0 to 2 and had a uniform
distribution. What is the probability that the rng value is 0.65 or larger?
a)
0.231
b)
0.325
c)
0.675
d)
0.769
7) The thermometer readings have a mean of 0℃ and a standard deviation of 1.00℃, and the readings are
normally distributed. Find the 93rd percentile of the thermometer readings.
a) 1.48℃
b) -1.48℃
c) 0.18℃
d) -0.18℃
8) Use the following data to find the minimum sample size required to estimate the population proportion.
Margin of error: 0.04; confidence level: 86%; 𝑝̂ 𝑎𝑛𝑑 𝑞̂ 𝑎𝑟𝑒 𝑢𝑛𝑘𝑛𝑜𝑤𝑛.
a) 108
b) 183
c) 343
d) 729
9) Suppose we have the following data to construct a confidence interval for the population mean: 95% confidence
level, n = 31, 𝜎 is unknown; population appears to be uniformly distributed. Determine which critical value
should be used to construct a confidence interval or state that neither critical value can be used.
a) 𝑧𝛼/2
b) 𝑡𝛼/2
c) Neither critical value can be used
10) Consider the following claim: The proportion of people aged 18 to 25 who currently use illicit drugs is equal to
0.20 (or 20%). Determine the correct null and alternative hypothesis.
a) 𝐻0 : 𝑝 = 0.20
b) 𝐻0 : 𝑝 ≠ 0.20
c) 𝐻0 : 𝑝 ≥ 0.20
d) 𝐻0 : 𝑝 ≤ 0.20
𝐻1 : 𝑝 ≠ 0.20
𝐻1 : 𝑝 = 0.20
𝐻1 : 𝑝 < 0.20
𝐻1 : 𝑝 > 0.20
11) When conducting the hypothesis testing with a significance level of 𝛼 = 0.05 for the claim from problem 10.),
the p-value = 0.0562. What is the correct conclusion?
a) Reject H0. There is sufficient evidence to reject the claim that the proportion of people aged 18 to 25 who
currently use illicit drugs is equal to 20%
b) Reject H0. There is not sufficient evidence to reject the claim that the proportion of people aged 18 to 25
who currently use illicit drugs is equal to 20%
c) Fail to Reject H0. There is sufficient evidence to reject the claim that the proportion of people aged 18 to 25
who currently use illicit drugs is equal to 20%
d) Fail to Reject H0. There is not sufficient evidence to reject the claim that the proportion of people aged 18 to
25 who currently use illicit drugs is equal to 20%
Solutions:
1. a.) 0.8230
b.) 𝜇𝑥̅ = 12, 𝜎𝑥̅ = 0.033
c.) .9999 ± 0.0001
2. a.) E = 0.073
b.) (.158, .303)
c.) We are 90% confident that the confidence interval (0.158, 0.303) actually does contain the true value of the
population proportion p.
3. a.) t = 2.861
b.) 190.64 (calc: 190.58)
c.) (1392, 1774)
4. 𝐻0 : 𝑝 = 0.24
𝐻1 : 𝑝 ≠ 0.24
𝛼 = 0.01
Test statistic: z = 1.66
p – value = 0.0485
𝑧𝑐𝑟𝑖𝑡 = 2.33
5. a.) t = -5.77
b.) p-value = 0.0000
c.) 𝑡𝑐𝑟𝑖𝑡 = −1.29
Multiple choice
6.) C
7.) A
8.) C
9.) B
10.) A
11.) D