# HCCC The Best Point Estimate of The Mean in Statistics Question

Description

1.) Video Games:In a recent study of 35 students, the mean number of hours per week
that they played video games was 16.6. The standard deviation of the population
was 2.8. (2 pts.)
(a) Find the best point estimate of the mean.
(b) Find the 95% confidence interval of the mean of the time playing video games and
verify that 35 students is a large enough sample for this interval estimate.
(c) Find the 99% confidence interval of the mean time playing video games.
(d) Which is larger? Explain why.
(e) Explain how the sample size affects the confidence interval.
2.) Gasoline: A random sample of state gasoline taxes (in cents) is shown below for 12
states. Use the data to estimate the true population mean gasoline tax with 90%
confidence. Does your interval contain the national average of 44.7 cents? (2 pts.)
38.4
38
40.9
43.4
67
50.7
32.5
35.4
51.5
39.3
43.4
41.4
Source: http://www.api.org/statistics/fueltaxes/
3.) Voters: Thirty-five percent of adult Americans are regular voters. A random sample of
250 adults in a medium-size college town were surveyed, and it was found that 110 were
regular voters. (a) Estimate the true proportion of regular voters with 90% confidence and
(b) show that 250 adults was a large enough sample for this interval estimate. (1 pt.)
4.) In a Sallie Mae survey of 950 undergraduate students, 53% take online course. The
sample results are n = 950 and
= 0.53.
(a) Find the margin of error E that corresponds to a 95% confidence level.
(b) Find the 95% confidence interval estimate of the population proportion p.
(c) Based on the results, can we safely conclude that more than 50% of undergraduates
take online courses?
(d) Assuming that you are an online reporter, write a brief statement that accurately
describes the results, and include all of the relevant information.
5.) problem #11 page 354 in your textbook and Appendix B Data Set 3 is needed.
11. Mean Body Temperature Data Set 3 “Body Temperatures” in Appendix B includes a
sample of 106 body temperatures having a mean of 98.20°F and a standard deviation of
0.62°F. Construct a 95% confidence interval estimate of the mean body temperature for the
entire population. What does the result suggest about the common belief that 98.6°F is the
mean body temperature?
6) According to the US Census Bureau, 46.1% of US citizens who are between the ages of
18 and 29 voted in the 2016 election, which was the highest voter turnout of the 21st
century. Suppose we believe that percentage for 18-29 year old adults is higher for Saint
Peter’s 18-29 year old adults students for the 2020 presidential election. To determine if
our suspicions are correct, we collect information from a random sample of 500 Saint
Peter’s students. Of those, 480 were citizens and were between the age of 18 and 29 in
time for the election (eligible to vote). Of those who are between 18-29 years old, 258
(53.75%) say that they did vote. Based on this random sample, do we have enough
evidence to say that the percentage of students between the ages of 18-29 and did vote
in the 2020 presidential election was higher than the proportion of 18-29 year old US
citizens who voted in the 2016 election? (1 pt.)
7) In the population of Americans who drink coffee, the average daily consumption is 3
cups per day. Saint Peter’s University wants to know if their students tend to drink less
coffee than the national average. They ask a random sample of 50 students how many cups
of coffee they drink each day and found
and s=1.5. Is there enough evidence that
their students drink less coffee than the national average? (1 pt.)
8) The screen time habits of 30 children were observed. The sample mean was found to be
48.2 hours per week, with a standard deviation of 12.4 hours per week. A company claims
that the standard deviation is 16 hours per week. A group of parents claim that the
standard deviation is not 16 hours per week. Test the claim that the standard deviation
was not 16 hours per week. (1 pt.)
9) A dermatologist wishes to estimate the proportion of young adults who apply sunscreen
regularly before going out in the sun in the summer. Find the minimum sample size
required to estimate the proportion to within two percentage points, a 90% confidence. (1
pt.)
10) Determine if the following is a Type I Error or Type II Error. Explain your answer.
A man goes to trial where he is being tried for stealing a car.
We can put it in a hypothesis testing framework. The hypotheses being tested are:
● H0 : Not Guilty
● Ha : Guilty
If the man did steal the car, but was found not guilty and was not punished, what type of
error is this situation? (1 pt.)