Part A -
Q1. Using two independent samples, two population means are compared to determine if a difference exists. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value?
A. 27
B. 12
C. 36
D. 15
Q2. What are the critical z-values for a two tailed hypothesis test if "alpha equals 0.01"?
A. plus-or-minus 1.96
B. plus-or-minus 2.33
C. plus-or-minus 2.58
D. plus-or-minus 1.65
Q3. A market research company checks whether prices of a certain product in different cities are different from the national average price by collecting a sample of local retailers and performing a hypothesis test.
The researchers wish to be able to detect a difference in price of $10. At a 5% significance level and with a sample size of 30, they found power of their test is only 50%. Their best course of action is to:
A. settle for only being able to detect a difference of $100 or more
B. increase the level of significance to 0.20
C. increase the sample size until the power is at least 80%
D. perform their test as is - power is not important
Q4. Facebook publishes some statistics about their users, and last year reported that the mean number of pages, groups and events that users join is 80, with a standard deviation of 48.
A random sample of 64 Facebook users were found to have joined on average 86 pages, groups, and events. Can we conclude that Facebook usage has changed since last year?
a) State your null and alternative hypotheses.
b) Perform a hypothesis test at the α = 0.05 significance level.
c) State the conclusion of your test, including the p-value.
Q5. In 2010 the Pew Research Center reported that teenagers send on average 50 text messages every day.
A researcher suspects this number is out of date, and wishes to determine if teens are sending fewer texts than they used to. A random sample of 25 teens were found to be sending an average of 47.75 texts per day. with a standard deviation of 15. What can the researcher conclude?
a) State your null and alternative hypotheses.
b) Perform a hypothesis test at the α = 0.10 significance level.
Part B -
Q1. Suppose we want to estimate to within $1000 the mean salary of all college graduates who were business majors. How many business majors would we sample to estimate the mean salary to within $1000 with 95% confidence, given a population standard deviation of 5000?
Q2. A College Board reports that the scores for college math preparation are as follows:
|
Outstanding
|
50
|
|
Very Good
|
46
|
|
Good
|
38
|
|
Needs Improvement
|
26
|
An independent researcher claims that the scores are evenly distributed among the four categories. Test the null hypothesis that there is no significant different among the scores with a .01 level of significant.
Q3. A 2016 study reported in a science magazine stated that college math teachers scored a mean of 3.4 points for providing feedback to students on their work. Assume the sample size was 26 and the sample standard deviation was 1.5.
a. Give the best point estimate for the population.
b. Construct a 90% confidence interval for the true population mean.
Q4. Within a certain country, there is a population of roughly ten million registered drivers. Of those registered drivers, 46% have admitted that it is not unusual to drive while being distracted. An independent researcher has decided to see if a recent campaign has helped remedy the issue. Of the 5,000 people questioned, 41% said it is not unusual to drive while being distracted. Using the Proportional Hypothesis Testing with 0.05 level of significace, has the recent campaign worked to lower the rates?
Q5. According to a specific social media website, the mean number of connections that users have is 70. A random sample of 50 users showed a mean of 75 connections. Assume the population standard deviation is 25. Test at a 5% significance whether the population mean number of connections is greater than 70. Use both the critical region and P-value techniques.
Q6. An online study showed the mean number of text messages sent and received daily by any given customer is 65. Suppose another researcher disputes this finding and is interested in testing whether the population mean number of text messages differs from 65. A random sample of 30 users yields a sample mean of 55.5 texts messages, with a standard deviation of 16. Perform both a critical region hypothesis test and P-value hypothesis test using a significance of 10%.
Q7. Below are the summary statistics for female verses male body temperatures in Fahrenheit
|
Gender
|
Sample Size
|
Sample Mean body temperature
|
Sample standard deviation
|
|
Females
|
27
|
98.394
|
0.743
|
|
Males
|
13
|
98.015
|
0.699
|
Using a 5% significance test the hypothesis that female body temperature is the same as male body temperature.