Statistics Questions: Observation vs Experiment, Confidence Interval, Mean, Median, Outliers, Popula

Question 1: Observation vs Experiment

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? 

2.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. 

3.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!)

4.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

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

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:

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

Orange  Blue     Green

0.9030.8380.911

0.920.8751.002

0.8610.870.902

1.0090.9560.93

0.9710.9680.949

0.8980.89

0.9420.902

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? 

Question 2: Confidence Interval

7.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? 

8.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? 

9. 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. (use the z for .95 confidence int.)

10.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?

11.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.

Question 3: Mean and Median with Outliers

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? 

12.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?

13.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.

14.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. 

15.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

16. 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

17. 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. 

Number of facebook friends

Weight in pounds

18.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

19.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 taken find 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

20.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?