Statistics homework help. STAT 3300 Homework #3
Due Tuesday, 05/19/2020
Note: Answer these questions on a separate piece of paper. In the top right corner, include
your name, SMU ID, and course number. Please include a title for the assignment so that
it is clear to the graders. If you miss class the day the assignment is turned in, submit this
before class in order to receive credit.
Question 1 (15 points total, 5 points each)
A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked
whether or not during the past 30 days they had used their phone while in a store to call a friend or family
member for advice about a purchase they were considering. The poll surveyed 1003 adults living in the
United States by telephone. Of these, 462 responded that they had used their cell phone while in a store
within the last 30 days to call a friend or family member for advice about a purchase they were considering.
a) Identify the sample size and the count.
b) Calculate the sample proportion.
c) Explain the relationship between the population proportion and the sample proportion.
Question 2 (20 points total, 5 points each)
Refer to the previous exercise.
a) Report the sample proportion, the standard error of the sample proportion, and the margin of error for
95% confidence.
b) Are the guidelines for when to use the large-sample confidence interval for a population proportion
satisfied in this setting? Explain your answer.
c) Find the 95% large-sample confidence interval for the population proportion.
d) Write a short statement explaining the meaning of your confidence interval.
Question 3 (14 points total)
A study of young children was designed to increase their intake of whole-grain, rather than regular-grain,
snacks. At the end of the study, the 86 children who participated in the study were presented with a choice
between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 48
children. You want to examine the possiblity that the children are equally likely to choose each type of snack.
a) (4 points) Formulate the null and alternative hypothesis for this setting.
b) (4 points) Are the guidelines for using the large-sample significance test satisfied for testing this null
hypothesis? Explain your answer.
c) (6 points) Perform a signficance test and summarize your results. In deciding how to show your work,
use the examples provided in class as a guide.
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Question 4 (15 points total, 5 points each)
Explain what is wrong with each of the following:
a) An approximate 90% confidence interval for an unknown proportion p is pˆ plus or minus its standard
error.
b) You can use a significance test to evaluate the hypothesis Ho : pˆ = 0.3 versus the one-sided alternative.
c) The large-sample significance test for a population proportion is based on a t statistic.
Question 5 (16 points total, 4 points each)
In each of the following cases, state whether or not the Normal approximation to the binomial should be
used for a significance test on the population proportion p. Explain your answers.
a) n = 30 and Ho : p = 0.3.
b) n = 60 and Ho : p = 0.2.
c) n = 100 and Ho : p = 0.12.
d) n = 150 and Ho : p = 0.04.
Question 6 (10 points total)
A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two
unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60
subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly
chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the
population who prefer fresh-brewed coffee.)
a) (5 points) Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the
large-sample z statistic and its p-value. You may skip the conclusion and sketch, as they are specifically
address in the next two parts of the question.
b) (3 points) Draw a sketch of a standard Normal curve and mark the location of your z statistic. Shade
the appropriate area that corresponds to the p-value.
c) (2 points) Is your result significant at the 5% level? What is your practical conclusion?
Question 7 (5 points total)
One of your employees has suggested that your company develop a new product. You decide to take a random
sample of your customers and ask whether or not there is interest in the new product. The response is on a 1
to 5 scale with 1 indicating “definitely would not purchase”; 2, “probably would not purchase”; 3, “not sure”;
4, “probably would purchase”; and 5, “definitely would purchase.” For an initial analysis, you will record the
responses 1, 2, and 3 as No and 4 and 5 as Yes. What sample size would you use if you wanted the 95%
margin of error to be 0.25 or less?
Question 8 (5 points total)
You are planning an evaluation of a semester-long alcohol awareness campaign at your college. Previous
evaluations indicate that about 20% of the students surveyed will respond Yes to the question “Did the
campaign alter your behavior toward alcohol consumption?” How large a sample of students should you take
if you want the margin of error for 95% confidence to be about 0.07?
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Statistics homework help