Math 243 - Introduction to Statistics Name:
Exam III – Practice Test – Longer than a “real” test!
What is OK? Calculator. Scratch Paper OK. Pencil recommended.
NOT OK: Notes, books, formula card, friends, cell phones, etc...
Formulas you might want:
1. For each confidence interval described below, circle which is the appropriate critical value to use: z* or t* and its value.
a. 95% confidence, n = 38, σ = 2.3, SRS: z* or t* , value=_____
b. 99% confidence, n = 38, σ unknown, SRS: z* or t* , value=_____
c. 95% confidence, n = 20, σ unknown, SRS: z* or t* , value=_____
d. 90% confidence, n = 400, p =.45, SRS: z* or t* , value=_____
e. 90% confidence, n = 100, p =.05, Plus 4: z* or t* , value=_____
2. A researcher measured the weight of back-packs of 25 randomly selected college students. The researcher reported a 95% confidence interval:
a. What symbol goes in the interval? ______
b. What does that symbol represent?
c. What is the symbol for the point-estimate and its value?___ = ___
d. Calculate the margin of error? ME = ______
e. Did the researcher use z* or t*? _____ = _____
f. What is the symbol for the sample standard deviation and its value? __=___
g. What is the value of the standard error? SE = ______
3. HOW LONG DO DOGS LIVE? Data were collected on the lifespan of medium size dogs. Analysis of the data showed that 36 randomly selected dogs had an average lifespan of 13.2 years. Assume that previous studies had shown the standard deviation for the lifespan of dogs to be 2.6 years.
a. Show how to calculate a 95% confidence interval for the mean lifespan of medium size dogs.
b. Use your result to write a confidence statement.
4. Mindy, Tesha, and Wes independently select random samples from the same population. The sample sizes are 100 for Victoria, 30 for Andrew, and 50 for Sarah. Each researcher constructs a 95% confidence interval. Match the following margins of error with the correct researcher:
1.10 1.55 2.00
5. TJ guesses the color of a card correctly 50 times in 100. He then calculates three confidence intervals. The confidence levels are 90%, 95%, and 99%. Match the each confidence interval below with the confidence level:
(.42, .58) (.40, .60) (.37,.63)
6. Circle the correct answer(s). Sara is interested in whether men or women spend more time studying.
a. Write the null and alternative hypothesis mathematically:
Ho: ______HA: ______
b. She collects a simple random sample the time spent by men and women studying and calculates the necessary statistics. She reports in her study that women spend a statistically significant more time studying than men (p-value = 0.08). She attributes this difference to her belief that women are more academically mature than men of the same age. She also reports a confidence interval. Circle any of the four confidence interval(s) below that could have been correctly reported.
95% Confidence Interval: (-2.2, 10.2) 95% Confidence Interval: (1.1, 13.1)
90% Confidence Interval: (-3.2, 12.6) 90% Confidence Interval: (0.4, 15.8)
7. ODOT engineer Drs. Smith and Urquidez did a small pilot study of the Highway 99 and Oakville Road intersection. They wrote down the following times in seconds between when a car turns onto Oakville Road and a car on Highway arrives at the intersection:
1.6 2.3 .8 1.4 .8 4.1 5.2 1.1 0.4 2.5 1.0 3.2
a. What is the sample mean? ______
b. What is the sample standard deviation? ______
c. What is the sample size? ______
d. Which critical value is appropriate at the 99% level? What is its value? ____ = _____
e. Write the appropriate general formula for a confidence interval of the population mean, then substitute the values into the formula and calculate the 99% confidence interval. Write a confidence statement.
f. Name two actions that could be taken in a future study to reduce the margin of error.
8. A random sample of 300 LBCC students found that 8 had been diagnosed with H1N1 (Swine Flu) during the month of October. Write a 95% confidence interval for the percentage of all LBCC students who had swine flu in October.
9. For each scenario below make the appropriate decision regarding the null hypothesis.
Scenario / Decisionα = .01, p-value = .04
α = .05, p-value = .04
α = .10, p-value = .04
90% confidence interval
Two-sided test
p-value = .08
α = .05, t value = 1.82
one-sided test
n=15
90% confidence interval
(.391, .458)
α = .01, t value = 3.01
two-sided test
n=21
95% confidence interval
Two-sided test
p-value = .06
90% confidence interval
(32.1, 34.8)
10. Recently there has been interest in the amount of weight children carry in their backpacks as to they go off to school. Data was collected on a random sample of 20 middle-school (mean= 8.5 lbs, s = 2.4) and 20 college students (mean = 10.5 lbs, s=3.6). Is the amount of weight children carry different from that carried by college students?
In Words Mathematically
Ho:______Ho: ______
HA:______HA: ______
11. Beer in pubs is often sold by the “pint” (16 ounces). But, perhaps their mugs contain less than 16 ounces of beer? The amount of beer in a pub’s mug was measured at 18 randomly selected pubs in Portland. The sample mean was 15.1 ounces with a standard deviation of 1.4 ounces.
In Words Mathematically
Ho:______Ho: ______
HA:______HA: ______
12. Fascinated by the question of whether a piece of toast lands more often or not with the butter side down, food scientist Dr. Kitto pushes 1200 buttered pieces of toast from the counter and counts 630 landing with butter side down!
In Words Mathematically
Ho:______Ho: ______
HA:______HA: ______
13. A total of 400 radish seeds were randomly divided evenly between either a low pH or a high pH environment. The number of radish seeds that germinated in a 5 day span was 75 in the low pH and 25 in the high pH environment.
In Words Mathematically
Ho:______Ho: ______
HA:______HA: ______
14. Analyze the results of each experiment: #11, 12, and 13 above. Choose your own alpha make a decision regarding the null hypothesis.
15. Suppose you are interested in whether you can make bouncy balls even more bouncy by heating them for five minutes with a hair dryer. You drop 16 balls twice from a height of 72 inches – once at normal temperature and once after being warmed. Balls are randomly assigned to being warmed first and then normal or normal first and then warmed.
Ball / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Normal / 54 / 58 / 59 / 56 / 61 / 50 / 63 / 58
Warmed / 62 / 56 / 62 / 63 / 62 / 60 / 61 / 65
Write a hypothesis statement mathematically, analyze the results at = .05, and draw conclusion.