# What type of study is this (observation or experiment), what is the variable of interest?

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.

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1. An admissions advisor for a local college decides he would like to determine the average age of students at the college for some promotional materials. To do this he pulls the records of 200 random students at the college.

What type of study is this (observation or experiment), what is the variable of interest?

1. Fifty registered nurses are asked how many hours they work each week. Based on this sample the estimated average is 46 hours with a margin of error of 4.9 hours. Use the given values to identify the confidence interval likely to contain the actual population mean.
2. The following histogram represents the movie lengths hit movies in 1998

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?

1. A real estate agent records the price of the eight homes she has listed at this moment they are as follows:

123,000 155,000 139,000 140,000 159,000 34,000 121,000 and

434,000

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!)

1. In a survey of 2,150 US teachers it was found that 60% of them said if they could start their careers again they would choose a different career. The margin of error was 5 percentage points

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

1. The following table shows the average weight and standard deviation for different colored M and M’s in grams

Color

Mean

Standard deviation

Red

0.91

0.03

Yellow

0.92

0.03

Blue

0.90

0.02

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

Red:

Yellow:

Blue:

1. The following table measures the weight of M and M’s (in grams) of various colors of the candy.

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

0.898 0.89

0.942 0.902

0.897

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?

1. A statistics student decided to roll a dice 50 times, she rolled the number two 11 times. Is the difference between what the student rolled and what is theoretically expected statistically significant?
2. Data was recorded for the number of home runs hit for three baseball players, Mark McGwire, Sammy Sosa and Barry Bonds. The Analysis of Variance results obtained from software are found below. The significance level is 0.10 in testing the null hypothesis.

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?

1. A researcher wishes to estimate the average number of hours that high school students spend on facebook each day. A margin of error of 0.22 hours is desired. Past studies suggest a population standard deviation of 2.1 hours is reasonable, estimate the minimum sample size needed to estimate the population mean with the desired accuracy.
2. A study was done among 1200 Walden Students. Among these students 700 were Masters of Nursing students and 520 of these were taking their first online course. Among the 500 other students, 410 were taking their first online course.

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?

1. On research study of illegal drug use among teenagers shows a decrease from 11.4% in 1997 to 9.5% now. Suppose a study in a large high school reveals that in a simple random sample of 1054 students 97 report using illegal drugs. Use the 0.05 significance level to test the principal’s claim that illegal drug use is below the national average.

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?

1. Suppose you know the distribution of sample proportions in samples of 300 registered voters who will vote for candidate A is normal with a mean of 0.34 with a standard deviation of 0.02. Suppose you select a random sample of 300 voters and find the proportion of those willing to vote for candidate A is 0.38.

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?

1. You select a random sample of n=15 families in your neighborhood and find the following family sizes.

7

8

11

10

9

7

8

8

7

8

7

8

9

10

6

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?

1. Given the following hypothesis statements:

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.

1. A simple random sample of 25 student IQ scores is selected. The average score is 102.5 with a standard deviation of 12.8. Us the t distribution to construct a 95% confidence interval for the population mean.

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

1. Assume that the population mean is to be estimated from a sample. Use the sample results to approximate the margin of error and 95% confidence level.

Sample size=121 sample mean=80 sample standard deviation =14

1. A simple yes/no survey is presented to two groups of subjects, those with children and those without. The results are summarized in the two way table below.

Yes

No

Respondent has children

190

240

Respondent does not have children

35

80

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?

1. In a recent study of 353 4 year old girls the following data was collected:

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. A high school student rolls a dice 12 times and records the following results

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)

Number

Frequency

Relative frequency (as a %)

Cumulative frequency

1

2

3

4

5

6

1. Assume the average weight of 5 year olds is normally distributed with a mean of 45 pounds and standard deviation of 5 pounds. Using the 68-96-99.7 rule find the following:

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

1. Determine if the following variable is qualitative or quantitative and give their level of measurement. If it is quantitative in nature stat if it is continuous or discrete.

Weight in pounds

1. The amount of income people save on average has decreased from 7% to 4%.

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%

1. Based on data from the college board assume SAT scores are normally distributed with a mean of 1518 points an d a standard deviation of 325 points.

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

1. A simple random sample of 16 different cereals is obtained; the sugar content (in grams) is measured for each cereal. The sample has a mean of 0.295 grams, a standard deviation of 0.168 grams. Use the 0.05 level of significance to test the claim that the mean amount of sugar is less than 0.3 grams.

a. State the null and alternative hypothesis statements

b. Find the test statistic T

c. Which hypothesis does the data support?

1. A random sample of thirty six cans of cola has a mean of 12.19 ounces with a standard deviation of 0.11 ounces. Assume we are using a 0.05 level of significance to test the hypothesis the average can of cola contains more than 12.19 ounces. The population mean is 12 ounces.

a. Find the test statistic z

b. Find the p value

1. The following data set includes the selling prices of homes (in thousands) and the amount of taxes paid

Selling Taxes

142 3167

175 4033

129 1471

138 3204

232 3513

135 3028

150 3131

207 5158

Find the r and r squared values

1. A population mean is to be estimated from the sample described below. Find the margin of error and 95% confidence interval.

Sample size 100, sample mean 75.0 sample standard deviation 10.0

1. The following table gives the homerun distances of ten home runs hit by Sammy Sosa and Mark McGwire. Find the range and standard deviation for each player

McGwire

Sosa

360

371

370

350

370

430

430

420

420

430

340

434

460

370

410

420

440

440

410

410

1. In a Gallup poll targeting 1025 randomly selected adult Americans 47% believed that the nations best years were still ahead of us (rather than behind us). Identify the following:

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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