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Section 8-2
Steps in Hypothesis Testing – Traditional Method
Chapter 8Hypothesis Testing
Example 1
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Using the z table find the critical value (or values). = 0.01
Section 8-2 Exercise #12b
Left tail
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Using the z table find the critical value (or values). = 0.05
Section 8-2 Exercise #12g
Right tail
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Using the z table find the critical value (or values).
= 0.01Two - tailed test.
Section 8-2 Exercise #12h
Section 8-3
z Test for a Mean
Chapter 8Hypothesis Testing
Example 2
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A report in USA TODAY stated that the average age of commercial jets in the United States is 14 years. An executive of a large airline company selects a sample of 36 planes and finds the averageage of the planes is 11.8 years. The standard deviation of the sample is 2.7 years. At = 0.01, can it be concluded that the average age of the planes in his Company is less than the national average?
Section 8-3 Exercise #5
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Section 8-3
Exercise #7
Chapter 8Hypothesis Testing
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The average one-year-old (both sexes) is 29 inches tall. A random sample of 30 one-year-olds in a large day care franchise resulted in the following heights. At = 0.05, can it be concluded that the average height differs from 29 inches?
25 32 35 25 30 26.5 26 25.5 29.5 32
30 28.5 30 32 28 31.5 29 29.5 30 34
29 32 27 28 33 28 27 32 29 29.5
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Section 8-3
Exercise #13
Chapter 8Hypothesis Testing
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To see if young men ages 8 through 17 years spend more or less than the national average of $24.44 per shopping trip to a local mall, the managersurveyed 33 young men and found the average amount spent per visit was $22.97.The standard deviation of the sample was $3.70. At = 0.02, can it be concluded that the average amount spent at a local mall is not equal to the national average of $24.44.
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Section 8-3
Exercise #17
Chapter 8Hypothesis Testing
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A study found that the average stopping distance of a school bus traveling 50 miles per hour was 264 feet (Snapshot, USA TODAY, March12, 1992). A group of automotive engineers decided to conduct a study of itsschool buses and found that for 20 buses, the average stopping distance of buses traveling 50 miles per hour was 262.3 feet.The standard deviation of the populationwas 3 feet. Test the claim that the average stopping distance of the company’s buses is actually less than 264 feet. Find the P-value. On the basis of the P-value, should the null hypothesis be rejected at = 0.01? Assume that the variable isnormally distributed.
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Section 8-4
t Test for a Mean
Chapter 8Hypothesis Testing
Section 8-4
Exercise #3a
Chapter 8Hypothesis Testing
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Find the critical value (or values) for the t test for each.
Right - tailed = 0.05
d.f . = 9 C.V . = + 1.833
n = 10
Section 8-4
Exercise #3b
Chapter 8Hypothesis Testing
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Two - tailed
n = 18
= 0.10
Find the critical value (or values) for the t test for each.
Section 8-4
Exercise #3c
Chapter 8Hypothesis Testing
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Left - tailed
n = 6
= 0.01
Find the critical value (or values) for the t test for each.
Section 8-4
Exercise #7
Chapter 8Hypothesis Testing
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The average salary of graduates entering the actuarial field is reported to be $40,000. To test this, a statistics professor surveys 20 graduates and finds their average salary to be $43,228with a standard deviation of $4,000. Using = 0.05, has he shown the reported salary incorrect?
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Section 8-4
Exercise #9
Chapter 8Hypothesis Testing
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A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at least 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown:
485 511 841 725 615520 535 635 616 582At = 0.025, is there enough evidence to reject the claim?
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Example 3
Section 8-4
Exercise #13
Chapter 8Hypothesis Testing
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Last year the average cost of making a movie was $54.8 million. This year, a random sample of 15 recent action movies had an average production cost of $62.3 million with a variance of $90.25 million.At the 0.05 level of significance, can it be concluded that it costs more than average to produce an action movie?
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Section 8-4
Exercise #17
Chapter 8Hypothesis Testing
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A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selected 20 women and the following data was obtained.
At = 0.05 can it be concluded that the average is still 5.8? Use the P - value method.
3 2 1 3 7 2 9 4 6 6
8 0 5 6 4 2 1 3 4 1
0 1: = 5.8 (claim) : 5.8H H
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Section 8-5
z Test for a Proportion
Chapter 8Hypothesis Testing
Section 8-5
Exercise #7
Chapter 8Hypothesis Testing
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It has been reported that 40% of the adult population participates in computer hobbies during their leisure time. A random sample of 180 adults found that 65 engaged in computer hobbies. At = 0.01, is there sufficient evidenceto conclude that the proportion differsfrom 40%?
0 1H = 0.40 H 0.40 ( ): p : p claim
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Section 8-5
Exercise #9
Chapter 8Hypothesis Testing
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An item in USA TODAY reported that 63% of Americans owned an answering machine. A survey of 143 employees at a large school showed that 85 owned an answering machine. At = 0.05, test the claim that the percentage is the same as stated in USA TODAY .
0 1H = 0.63 ( ) H 0.63: p claim : p
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Section 8-5
Exercise #15
Chapter 8Hypothesis Testing
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Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, with an enrollment of 300 students, a study found that 50 studentssmoked at least one pack of cigarettes a day. At = 0.05, test the claim that 18% of all high school students smoke at least one pack of cigarettes a day. Use the P - value method.
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Section 8-5
Exercise #19
Chapter 8Hypothesis Testing
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A report by the NCAA states that 57.6% of football injuries occur during practices. A head trainer claims that this is too high for his conference, so he randomly selects 36 injuries and finds that 17 occurred during practices. Is his claim correct, using = 0.05 ?
0 1H 0 576 H : < 0.576 (claim)p p : .
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Section 8-6
2 Test for a Variance or Standard Deviation
Chapter 8Hypothesis Testing
Section 8-6
Exercise #5
Chapter 8Hypothesis Testing
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Test the claim that the standard deviation of the number of aircraft stolen each year in the United States is less than 15 if a sample of 12 years had a standard deviation of 13.6. Use = 0.05.
H1 : < 15 (claim) 0H : 15
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Section 8-6
Exercise #7
Chapter 8Hypothesis Testing
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The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.2 minutes or less. A sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.8 minutes. At = 0.01, test the claim that the standard deviation is less than or equal to 1.2 minutes. Use the P-value method.
0H : 1.2 ( )claim H1 : > 1.2
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Section 8-6
Exercise #9
Chapter 8Hypothesis Testing
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A random sample of 20 different kinds of doughnuts had the following calorie contents. At = 0.01, is there sufficient evidence to conclude that the standard deviation is greater than 20 calories?
290 320 260 220 300 310 310 270 250 230
270 260 310 200 250 250 270 210 260 300
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Section 8-6
Exercise #13
Chapter 8Hypothesis Testing
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A random sample of home run totals for National League Home Run Champions from 1938 to 2001 is shown. At the 0.05 level of significance, is there sufficient evidence to conclude that the variance is greater than 25?
34 47 43 23 36 50 42
44 43 40 39 41 47 45
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