Math 338 Midterm 1 Short Answer
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California State University, Fullerton *
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Course
338
Subject
Mathematics
Date
Apr 3, 2024
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7
Uploaded by PresidentCaribou4306
\CSUF Math 338 Spring 2020 Midterm 1 Short Answer Your name: __________________________________ Last Name, First Name Short Answer Directions
. You may use your calculator for this exam. You may not use any other electronic devices. You many use a 3 x 5 note card (double-sided). Please raise your hand if you have a question. You may write anywhere on the exam. Your scores (to be filled in by Ms. Morrow): Question 1 –
2: / 12 Question 3 –
6: / 12 Question 7 –
8: / 11 Question 9: / 10 Question 10 - 11: / 7 Question 12 –
13: / 8 Total: / 60 Short Answer Total _______ / 60 Lab Total _______ / 40 Midterm 1 Total _______/ 100
1.
[6 points] Twenty students in an introductory psychology class were selected by random sampling and asked to participate in an experiment to determine the effects of sunlight on sleeping patterns. Match each term with the appropriate response by labeling each with A, B, C, or D. a.
What is the experimental unit/subject? _____ b.
What is the explanatory variable? _____ c.
What is the response variable? _____ A.
The sunlight B.
Different sleeping patterns C.
The 20 students D.
The entire Psych class
2.
[6 pts] Suppose you want to determine if there are differences in the average prices among items at three local supermarket chains. a.
What type of study would work best? A)
Observational Study B) Experiment b.
If a block design were used, what would be an appropriate blocking variable for this study? (Choose One) A) A supermarket B) A type of item (e.g., beverages, medications, condiments, etc.) C) None of the above c.
To reduce bias, how should you select the items to use in your study? (Choose One) A) Choose items which you know are commonly purchased. B) Randomly select an appropriate number of times from a list of all possible items in the supermarket. C) Choose only brand-name items.
3.
[4 pts] A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions.
a.
The number 70.24% is a _________. (Choose One) A) statistic B) sample C) parameter D) population b.
What type of sampling method was used to collect the data? A) A simple random sample B) A stratified random sample C) Cluster sample D) Voluntary response 4.
[4 pts] Identify the following studies as Cross-Sectional, Retrospective, or Prospective. a.
A medical researcher follows smokers and nonsmokers for several years to identify differences in rates of cancer between the two groups. b.
A polling organization conducts a survey to determine current levels of support for different political candidates. 5.
[2 pts] Determine which are the correct mean and median for the following histogram. A)
Mean is 4.6; median is 5.0 B)
Mean is 4.5; median is 4.2 C)
Mean is 3.5; median is 4.3 D)
Mean is 6.1; median is 5.6 6.
[2 pts] The standard deviation can be negative. A)
True B) False
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7.
[6 pts] The time to complete an exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. a.
Using the Empirical rule, approximately what percentage of students will complete the exam in under an hour? b.
What is the z-score for a student that completed the exam in 78 minutes? c.
Explain what the z-score in part (b) represents in terms of the mean and standard deviation. 8.
[5 pts] Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. Define events A = {the next two babies are boys} and B = {at least one of the next two babies is a boy}. a.
What do we know about events A and B? (Choose One) A) They are disjoint. C) They are independent. B) They are complements. D) None of the above b.
What is the probability of event B?
9.
[10 pts] The table below describes the smoking habits of a group of asthma sufferers. Find the following probabilities for one randomly selected person.
Round probabilities to 3 decimal places.
Non smoker Occasional smoker Regular smoker Heavy smoker Total Men 411 45 86 30 572 Women 441 37 82 30 590 Total 852 82 168 60 1162 a.
the person is a woman? b. the person is a regular smoker? c.
the person is a woman and a regular smoker? d.
the person is a woman or a regular smoker? e.
the person is a regular smoker given that the person is a woman.
10.
[5 pts] If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M. a.
What is the probability of drawing a yellow candy? b.
If you select two M&M’s and the colors are independent, then what is the probability that both are the same color? 11.
[2 pts] The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. Suppose that at both schools a simple random sample of about 3% of the undergraduates will be taken. What can we conclude about the sampling variability for the sample proportion from Johns Hopkins as compared to that from Ohio State? (Choose One) A) The sample proportion from Johns Hopkins will have less sampling variability than that from Ohio State. B) The sample proportion from Johns Hopkins will have more sampling variability than that from Ohio State. C) The sample proportion from Johns Hopkins will have about the same sampling variability as that from Ohio State. D) It is impossible to make any statements about the sampling variability of the two samples because the students surveyed were different. Color Brown Red Yellow Green Orange Blue Probability 0.3 0.3 ? 0.1 0.1 0.1
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12.
[6 pts] Chromosome defect A occurs in only one out of 200 adult males. A random sample of 100 adult males is selected. Let the random variable X
represent the number of males in the sample who have this chromosome defect. a.
Verify that X is a binomial random variable and write the exact distribution of X. b.
Can we use the Normal approximation to answer probability questions about the random variable X? Briefly explain why or why not. 13.
[2 pts] The following histogram shows the distribution of 1000 sample observations from a population with a mean of 𝜇 = 4
and a variance of 𝜎
2
= 8
Suppose a simple random sample of 100 observations is to be selected from the population and the sample average x
is calculated. Which of the following statements about the distribution of x
is FALSE
? (Choose One) A)
The distribution of x
will have a mean of 4. B)
The distribution x
will be approximately Normal. C)
Because the distribution shown in the histogram above is clearly skewed to the right, the shape of the distribution of x
will also show skewness to the right. D)
Even though the distribution of the population variable appears to be skewed to the right, the distribution of x
will be approximately symmetric around 𝜇 = 4
. E)
The standard deviation of the distribution of x
will be 0.283. 0
10