Statistics
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samplemidterm.pdf
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Statistics II Sample Project/Practice Midterm Ch 10-14 Name__________________ Dr. C. Monticelli Show all work as done on my materials. Assume all populations normal. 1. a) The table below shows the weights of seven subjects before and after following a
particular diet for two months. Using a .01 level of significance, test the claim that the diet is effective in reducing weight.
Did you subtract before – after or after – before? ________________________
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 98% confidence interval for, . Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
Subject A B C D E F G Before 187 156 153 194 195 179 157 After 180 147 151 199 181 181 145
µd
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2. A random sample of 16 women resulted in blood pressure levels with a standard deviation of 21.9 mm Hg. A random sample of 17 men resulted in blood pressure levels with a standard deviation of 20 mm Hg. Use a .025 significance level to test the claim that the blood pressure level for women has a larger variance than those for men. Use women as group one.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
3. a) The Better Cookie Company claims its chocolate chip cookies have more chips than another chocolate chip cookie. 120 Better Cookies and 100 of the other type of cookie were randomly selected and the number of chips in each cookie was recorded.
At the .02 level of significance test the claim that the population of Better Cookies has a higher mean number of chips. Group one is Better Cookies.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
Better Another SampleMean#ChocChips 7.6 6.9
populationSD 1.4 1.7
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b) Construct a 96% confidence interval for . Interpret the interval.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret ________________________________________ 4. a) Test the claim that the mean for Sample A is less than Sample B at the .01 significance level. Assume both populations normal and the variances are equal.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 98% confidence interval for based on the sample data above. Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
µ1 − µ2
SampleA SampleB x1 = 24.7 x2 = 24.6
s1 = 5.7 s2 = 4.2 n1 =10 n2 =8
µ1 − µ2
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5 a) A sample of 50 randomly selected men with high triglyceride levels consumed 2 tablespoons of oat bran daily for 6 weeks. After 6 weeks, 60% of the men had lowered their triglyceride level. A sample of 80 men consumed 2 tablespoons of wheat bran for six weeks. After six weeks, 25% had lower triglyceride levels. Test the claim that there is a significant difference in the two proportions at the .01 level. Let Oat Bran be Group 1.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 99% confidence interval for . Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
p1 − p2
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6 a) Test the claim that populations A and B have equal means. Use the .05 level. Assume the variances are not equal and populations normal.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 95% confidence interval for . Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
SampleA SampleB n1 = 32 n2 = 37 x1 =130 x2 =160
s1 = 65 s2 = 30
µ1 − µ2
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7.Listed below are results from two different tests designed to measure productivity and dexterity for randomly selected employees.
a. Plot the scatter diagram below. Label x and y axes. Do a rough sketch.
b. Find the value of the linear correlation coefficient r by the TI83 shortcut- state calculator screen name
c) Test the claim of no linear relation by the TI83 p-value method. = .05
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________ d) Find the estimated equation of the regression line by TI83 shortcut e) Plot the regression line on the scatter diagram in part a). f) Assuming a significant linear correlation, predict the score a student would get on dexterity, given he got an 80 on productivity. g) What percentage of the total variation can be explained by the regression line?
Pr oductivity( x) 59 63 65 69 58 77 76 69 70 64 Dexterity( y) 72 67 78 82 75 87 92 83 87 78
α
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8. Responses to a survey question are broken down according to employment and the sample results are given below. At the .10 level of significance, test the claim that the response and employment are independent.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________ 9. In analyzing the random number generator of a certain computer, the following results were obtained. At the .05 significance level, test the claim that the outcomes occur with the percentages 20%, 10%, 15%, 15%, 20%, 20%.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
Yes No Undecided employed 15 35 20 unemployed 25 25 10
outcome 1 2 3 4 5 6 frequency 18 12 14 16 21 15
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10. At the .01 significance level, test the claim that the three brands have the same mean level if the following sample results have been obtained.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
BrandA BrandB BrandC 44 30 28 47 32 27 44 34 31 40 36 32 39 38 36
40 42
