Please take the time to review the following mathematical problems. If you have are able to solve these problems you will be in GOOD shape for your final exam.. You may check your solutions at the end of this document.
Remember you only have ONE attempt at the final exam MAKE IT COUNT!
Your exam is open note and open book please take advantage of the opportunity to use these resources
What type of study is this (observation or experiment), what is the variable of interest?
a How many movies total are represented in this histogram?
b. How many movies lasted less than 150 minutes?
c. How many movies lasted more than 150 minutes?
d. What is the highest possible movie length represented in this histogram?
123,000 155,000 139,000 140,000 159,000 34,000 121,000 and
a. Find the mean and median of the data presented
b. Identify the outlier on the LOW end of the data set, remove this value and calculate the new mean and median
c. Identify the outlier on the HIGH end of the data set, remove this value what is the new mean and median of the data set (HINT be sure you put your low value back in!)
What was the goal of this study
What is the population
Identify the population parameter of interest
Identify the sample
What is the raw data collected for this study
Identify the sample statistic
Based on the margin of error identify the range of values likely to contain the population parameter of interest
Assume the machine filling the bag is set to reject M and M’s more than 2 standard deviations above and below the mean
For each color find the range of weights that are acceptable to the vending machine
Orange Blue Green
0.903 0.838 0.911
0.92 0.875 1.002
0.861 0.87 0.902
1.009 0.956 0.93
0.971 0.968 0.949
Use a 0.01 level of significance to test the claim that the different colors all have the same mean.
a. Find the p value
b. At this level is there significant evidence to say that all colors have the same mean?
Source: DF: SS: MS: Test Stat Critical F: P-Value:
Treatment: 2 9546.87 4773.43 3.35 2.32 0.036
Error: 206 293224.08 1423.41
Total: 208 302770.95
What is the null hypothesis?
What is the alternative hypothesis
What is the p value
Is there sufficient evidence to support the claim that the three players have different average number of home runs hit?
a. What percentage of students were nursing students
b. What percentage of nursing students were taking their first online course
c. Among those who were NOT nursing students what percentage were taking their first online course?
d. What percentage of the students were taking the first online course?
a. formulate the null and alternative hypothesis
b. The sample statistics are the sample size n=1054 and the sample proportion , find the sample proportion rounded to four decimal places
c. Find the standard score, z for the sample proportion
d. Is there sufficient evidence to support the principals claim that the illegal drug use at this school is below the national average?
a. How many standard deviations is the sample proportion from the mean of the distribution of sample proportions?
b. What is the probability the selected sample would have a proportion of less than 0.38?
Find the mean family size from the sample as well as the standard deviation
What is the best estimate for the mean sample size for the population of all family sizes in the country?
What is the 95% confidence interval for the mean?
Do you feel this sample is representative of the entire nation why or why not?
Ho: The average GPA of males=average GPA of females
Ha: The average GPA of males is not equal to the average GPA of females
Explain in the context of GPA for males and females what it means to make a type I and type II error.
Solution: Margin of error = t * (s / SQRT n )
S = standard deviation value
SQRT = square root symbol
n = sample size
t = 2.064 (for this problem)
Find the t value with degree of freedom = 25-1 = 24 (or closest to 24 in the t table) and alpha 0.05 or 5%.
After you find the margin of error, add and subtract it from the given mean value to find the Confidence interval.
Confidence interval = mean value +/- margin of error value
Sample size=121 sample mean=80 sample standard deviation =14
Respondent has children
Respondent does not have children
a. State the null and alternative hypotheses
b. Find the table of expected frequencies
c. Find the chi squared test statistic
d. Find the critical value of the chi squared test statistic at a 0.05 level of significance
e. Based on these values which hypothesis is supported?
One of the girls weighed 40 pounds, she was heavier than 200 of the other girls. What percentile is this value?
One of these girls weighed 24 pounds, she was heavier than 18 of the other girls, what percentile was this particular value?
One of the girls weighed 44 pounds and was heavier than 301 of the other girls. What is the percentile of this particular value?
1 4 6 2 2 3 4 5 6 1 2 3
Based on these results complete the following table (round to the nearest tenth as needed)
Relative frequency (as a %)
a. Percent of five year olds who weigh less than 40 pounds
b. The percent who weigh more than 55 pounds
c. The percent who weigh between 40 and 55 pounds
Number of facebook friends
Weight in pounds
a. The savings rate has decreased by __ percentage points
b. Find the percent change in savings rate
Percent of change = (new income – original income) / original income
= (0.04 – 0.07) / 0.07
= 0.03 / 0.07
= 0.4285 = 42.85%
a. If a sample of 100 students is takenfind the mean and standard deviation of the distribution of sample means
b. If a sample of size 121 students is taken find the mean and standard deviation of the distribution of sample means
a. State the null and alternative hypothesis statements
b. Find the test statistic T
c. Which hypothesis does the data support?
a. Find the test statistic z
b. Find the p value
Find the r and r squared values
Sample size 100, sample mean 75.0 sample standard deviation 10.0
a. The sample
b. The population
c. The sampling method used
d. Identify the sample statistic
e. Identify the population parameter
f. Do you believe the sample is representative of the population? Why?
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