Stat 3001

Check your solutions from the practice. Please be sure you fully understand all solutions before taking your exam.

1 . a. The type of study is observational with the variable of interest being the age of the student.

2 . (41.1, 50.9)

3. a. 36 movies b . 29 movies c. 23 movies d. About 230 minutes

4. Part a: Median 139,500 Mean: 163,125 Part b: Outlier 34,000 Median: 140,000 Mean: 182, 000 Part c: outlier 434,000 Median: 139,000 Mean: 124,428.57

5 . a. The goal is to determine how many teachers would choose a different career if given the opportunity b . All US teachers c. Percentage of teachers who would choose a different career d. 2150 teachers who were questioned

e . Raw data is teacher responses (yes no) to question if they would choose a different career. f. 60% of teachers who said they would choose a different career g. 55%---65%

6. Red: (0.85,0.97) Yellow: (0.86, 0.98) Blue: (0.86,0.94)

7 . F ro m st at di sk Source: DF: SS: MS: Test Stat, F: Critical F: P---Value: Treatment: 2 0.00224 0.00112 0.505269 6.112108 0.612123 Error: 17 0.03769 0.002217 Total: 19 0.03993

Fail to Reject the Null Hypothesis There is not sufficient evidence to reject equality of means

The p value 0.61 We have sufficient evidence to claim the mean of all colors is the same.

8. Expected probability of rolling a 2: 0.16 Actual results: 0.44 Difference 0.28, this is statistically significant

9 . Null hypothesis: The mean of all three players are the same Alternative hypothesis: the mean of at least one player is different The p value is 0.036 At this level we must reject Ho and conclude at least one mean is statistically different.

1 0 . The minimum sample size is 365 students 1 1 . a. 58%

b . 74% c. 82% d . 7 8

1 2 . H0: p=0.095 a. Ha: P<---.095

b . P hat= 0.0920 c. Z=---0.33

d. No Test results from stat disk are as follows:

Claim: p < p(hyp)

Sample proportion: 0.0920304 Test Statistic, z: ---0.3288 Critical z: ---1.6449 P---Value: 0.3712

90% Confidence interval: 0.0773847 < p < 0.106676

Fail to Reject the Null Hypothesis Sample does not provide enough evidence to support the claim

1 3 . a. 2 standard deviations b . 97.72%

1 4. FROM STAT DISK: Descriptive Statistics Column 3

Sample Size, n: 15 Mean:8.2

Median: 8 Midrange: 8.5 RM S : 8.306624 Variance, s^2: 1.885714 St Dev, s:1.373213 Mean Abs Dev: 1.066667 Range: 5 Coeff. Of Var. 16.75%

Minimum: 6 1 st Quartile: 7 2 nd Quartile: 8 3 rd Quartile: 9 Maximum: 11

Sum: 123 Sum Sq: 1035

c. The best estimate for the mean is 8.2 people d. The 95% confidence interval is (from stat disk)

Margin of error, E = 0.7586815

95% Confident the population mean is within the range: 7. 44 1 3 1 9 < mean <8.958681

No this is not representative of the entire nation 1 5 . Type I error: reject the fact that males and females are equal in GPA when

that is in fact true Type II error--- Conclude the GPA of males and females are equal when that is not in fact true

1 6. (97.22,107.78) 1 7. From stat disk we have:

Margin of error, E = 2.519909

95% Confident the population mean is within the range: 7 7 .4 8 0 0 9 < mean <82.51991

1 8 . A. Null hypothesis: Survey response is independent of gender Alternative hypothesis: There is a relationship between survey response

and if the respondent has children b .

Y e s N o

Has Children 177.523 252.477 Does not 47.477 67.523

c . 7 . 1 0 3 d . 3 . 8 4

e . The data supports the alternative hypothesis. 1 9 . a. 57th percentile

b . 5th percentile c. 85th percentile

2 0 . Number Frequency Relative

frequency (as a Cumulative frequency

%) 1 2 16.7% 2 2 3 25% 5 3 2 16.7% 7 4 2 16.7% 9 5 1 8.3% 10 6 2 16.7% 12

2 1 . a. 16 b. 2.5% c . 81.5 %

2 2 . a Quantitative, discrete, ratio b . Quantitative, continuous, ratio

2 3 . a. ---3 percentage points b . ---4 2 . 9 %

2 4. a. Mean=1518 standard deviation=32.5 b . Mean= 1518 standard deviation= 29.5 2 5 . H0: μ=0.3

Ha : μ<0.3 B. t=---0.119 c. The data supports the null hypothesis

2 6. a. 10.4 b . Less than 0.0001

2 7 . From Stat disk: Sample size, n: 8

Degrees of freedom: 6

Correlation Results: Correlation coeff, r: 0.6652373 Critical r: ±0.706734 P---value (two---tailed): 0.07182

Fail to Reject the Null Hypothesis Sample does not provide enough evidence to support a linear correlation

Regression Results: Y= b0 + b1x:

Y Intercept, b0: 361.9401 Slope, b1: 18.20297

Total Variation: 7.497885e+6 Explained Variation: 3.318119e+6 Unexplained Variation: 4.179766e+6 Standard Error: 834.6423

Coeff of Det, R^2: 0.4425406 2 8 . Margin of error: 2.0 confidence interval (73,77) if using formula from book

Or from stat disk Margin of error, E = 1.984215

95% Confident the population mean is within the range: 73.01579 < mean <76.98421

2 9 . McGwire: Range: 120 Standard deviation 3 9.00 So sa: Range 90 Standard deviation 31.9

3 0 . Sample--- 1025 randomly selected adults Population: all adult Americans Sampling method: simple random sampling Sample statistic: 47% who believe the best years are ahead Population parameter: Amount of all Americ ans who believe the best years area ahead of us This sample is likely representative of the population due to the fact it is randomly selected and more than 1000 people are chosen