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Solved Examples
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eee Two laboratories carried out tests on five samples of ice cream to find out the fat content in it. What did the results show at 95% and 99% confidence levels?
 Lab A 7 9 8 10 8 Lab B 9 8 8 9 7
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eee A testing agency is comparing the rental costs of two car models in six different cities. At 99% confidence find the test value and check whether there is any difference in the rental costs.
 Model 1 (\$) 42 45 37 41 56 46 Model 2 (\$) 40 43 32 39 52 50

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eee The data corresponding to the cholesterol levels of eight persons before and after taking a mineral is shown. Find the test value. What can you say about their means at 95% confidence?
 Before (X1) 220 230 190 185 208 212 210 234 After (X2) 215 232 188 182 210 208 206 236
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eee At 99% confidence find the test value and verify if the means differ.
 Gentech 45 35 64 57 62 43 Control 43 39 62 50 54 52

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eee The data corresponding to the amount of rainfall(mm) in a state over a week measured by two recording stations is given. Find the test value and check whether they differ at 95% confidence level.
 Station A 2 1.5 1 3.1 2.5 4 2.5 Station B 1.8 1.7 1 3 2.4 4.1 2.8
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eee The data corresponding to the variation of the costs of lands (million dollars) in six states over a period of time is shown. Find the test value. Is the variation considerable at 99% confidence?
 1994 186 414 345 67 25 87 2004 162 430 350 60 30 83
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eee The data corresponding to the attitudes of six persons before and after watching a movie on exercise is given. A high value indicates a more favorable attitude towards exercise. At 99% confidence find the test value and check whether the means differ.
 Before (X1) 12 14 9 8 5 After (X2) 14 10 9 8 6

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eee A dietician claims that taking a special vitamin course can increase the physical strength of a person. The data corresponding to the weight(pounds) they are able to lift before and after taking the vitamin course is shown. Find the test value. Can you support his claim at 95% confidence?
 Before (X1) 200 210 240 250 235 After (X2) 210 205 250 255 225

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eee The owner of a restaurant claimed that the number of days the workers missed the work due to illness before a program is less than that after the program.The data is shown. Find the test value and verify if his claim is correct at 99% confidence.
 Before (X1) 2 6 3 5 3 1 2 After (X2) 1 4 8 3 1 5 3

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eee A seminar is given to the students of five classes of a school on the importance of communication skills. The number of students of each class who attended the communication skills development classes before and after attending the seminar are listed in the table. At 95% confidence, find the test value and verify if both the mean values differ.
 Before (X1) 20 22 25 28 30 After (X2) 28 18 29 36 28
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eee Blood cells of four females are tested with progesterone for cellular response. Find the test value and test if the mean progesterone response differs from that of the others at 99% confidence.
 Tested 5.65 2.18 1.32 2.45 Untested 5.12 1.2 1.1 1.42

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eee The students of a class were given a test in Statistics. Then they were given coaching for some days and the test was repeated. The results are as shown. Find the test value and check whether the performance improved at 99% confidence.
 Before (X1) 35 32 25 28 45 After (X2) 42 30 30 25 48
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eee The data corresponding to the level of red blood cells in men and women of 27 years of age is given. Find the test value and check whether the means differ at 99% confidence.
 Men 3.06 2.87 3.6 3.52 Women 1.34 1.7 2.9 1.5
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eee Find from the given data whether the annual percent salary increase of the CEO of a company is greater than the annual percent increase of the revenue of the company or not at 95% confidence. Give the test value.
 Revenue 25 14 16 18 10 CEO's salary 11 15 10 9 12

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eee The data corresponding to the number of leaves taken per year by married and unmarried employees of a company is shown. Find the test value and check whether both the means differ at 99% confidence.
 Married 50 52 60 46 Unmarried 56 48 62 40
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eee In a statistics class students were asked to determine if they sleep more number of hours on weekends than on weekdays. Five students gave the data shown. Check whether there is a difference in both the means at 95% and 99%.
 Weekdays 8 7.5 6 5.5 9 Weekends 10 9 9 8 12
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eee College students played two rounds of golf, one before and the other after the instructions were given. Find the test value. At 99% confidence did the scores improve?
 First round 80 78 72 69 68 72 Second round 78 82 75 72 65 73
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eee The data corresponding to the number of grammatical errors made by six students before and after introducing a new grammar program is given. Find the test value and check whether the errors reduced at 99% confidence.
 Before (X1) 12 8 5 4 0 2 After (X2) 8 4 1 1 0 0
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eee Six newly admitted students of a college are made to take a test. Seeing the results of the test, the Principal arranged a refreshment class for two hours. Again they were made to take the test. Find the test value. At 95% confidence did the refreshment class improve their performance?
 Before (X1) 10 12 15 14 18 20 After (X2) 13 14 15 16 20 20

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eee The senior surgeon of St. Ann's hospital claims that many patients who undergo heart surgery build up anxiety. Six patients were tested for anxiety before and after the surgery. The test results indicating the level of anxiety are tabulated. Find the test value and check whether his claim is correct at 99% confidence.
 Before 26 24 18 10 20 15 After 28 18 10 11 16 16
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eee For the data shown, find the test value and check whether the means differ at 95% confidence.
 First 45 67 23 78 Second 50 60 30 69

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eee The peak wind gusts (miles per hour) measured at four weather stations of a particular state in the months of January and February are shown. Find the test value and check whether the wind gusts in January are less than that in February at 95% confidence.
 January 140 135 128 138 February 112 125 135 148

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eee A physical education director claims that by taking a special vitamin, body weight can be increased. The data corresponding to the weights of five students before and after taking the vitamin is shown. Is there enough evidence to support his claim at 90% confidence? Find the test value.
 Before (kg) 78 86 75 72 82 After (kg) 82 84 77 75 80

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eee The pollution control department of a country conducted a survey to determine the pollution levels in different areas of two states. Find the test value and determine if the means differ at 99% confidence.
 State 1 45 34 76 29 State 2 56 28 80 16

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eee A researcher compares the pulse rates (number of beats per second) of six sets of twins to see if there is any difference. Find the test value and check if the means differ at 95% confidence level.
 Twin A 86 88 84 89 80 83 Twin B 82 89 84 86 86 85
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