Statistics Final Part 2

At a certain university, the average attendance at basketball games has been 3225. This year the attendance for the first 14 games has been 2815 with a standard deviation of 735. The athletic director claims that the attendance is the same as last year. If α= .05, what are the critical values for this two-tailed t test?

+/-2.16

The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed?Compute the test value?

-1.31

Using the z table, determine the critical value for the left-tailed test with α = 0.02.

-2.05

A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using α = 0.01?

-2.33

Find the critical value(s) for a two-tailed test with and draw a graph that illustrates your answer.

-2.33, 2.33 https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/HW8_20416130750/f1q2g4.jpg

Find the required χ2-value. For a χ2-curve with 27 degrees of freedom, find the χ2-value having area 0.01 to its right.

46.963

At a certain university, the average attendance at basketball games has been 3025. Due to the dismal showing of the team this year, the attendance for the first 13 games has averaged only 2615 with a standard deviation of 535. The athletic director claims that the attendance is the same as last year. What is the test value needed to evaluate the claim?

-2.76

349 people were asked if they were satisfied with their jobs. 34% said they were. H0: p = 0.42.

-3.028

A drug company claims that over 90% of all physicians recommend their drug. 800 physicians were asked if they recommend the drug to their patients. 39% said yes. H0: p = 0.9.

-48.08

A recent report by the American Medical Association stated the average annual salary of psychiatrists is $189,121 with a population standard deviation of $26,975. A group of hospital administrators randomly sampled 64 psychiatrists and found an average annual salary of $198,630. The group claims that the average annual salary is actually higher than what the American Medical Association reported. What is the P-value for this one-sided test?

0.0024

A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists this year yielded an average salary of $198,630. Is there evidence that the average salary is actually higher than what the American Medical Association reported? At , what is the p-value for a one-sided test?

0.0024

A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists this year yielded an average salary of $198,630. Is there evidence that the average salary is actually higher than what the American Medical Association reported? At o=0.05 , what is the p-value for a one-sided test?

0.0024

The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed? What is the p-value for this left-tailed test?

0.0951

If the sample mean is 11, the hypothesized population mean is 10, and the population standard deviation is 4, compute the test value needed for the z test.

0.25

According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. At α=0.05 , what is the test value?

0.30

Using the z table, find the critical value (or values) for an = 0.12 right-tailed test.

1.18

Out of 41 observations, 60% were successes. H0: p = 0.49.

1.409

A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. At α = 0.05, what is the critical value?

1.65

At , o=0.05 what is the critical value for a right tailed test?

1.65

Using the z table in Table E of Appendix C, determine the critical value for the right-tailed test with α=0.035.

1.81

Using the z table, determine the critical value for the right-tailed test with α = 0.035.

1.81

Find the required χ2-value. For a χ2-curve with 7 degrees of freedom, find the χ2-value having area 0.05 to its right.

14.067

A population is normally distributed with a standard deviation . We wish to test the hypotheses H0: μ = 1152.7; . A 105-item sample has a mean = 1189.8. Compute the value of the test statistic.

14.35

An average department store sells 300 men's suits per year. The men's suit departments at a particular national chain of stores claim they sell more than the industry average. In 35 of their stores, they sold, on the average, 380 suits per year with a population standard deviation of 30. What is the test value for their claim?

15.78

At a certain university, the average attendance at basketball games has been 2700 spectators per game. The attendance for the first 15 games has been 2500 spectators per game with a standard deviation of 650. The athletic director claims that the attendance is the same as last year. If α = .05, what are the critical values?

2.145

What is the critical t-value for a right-tailed test when α=0.025 and d.f.= 12?

2.179

What is the critical value for a right-tailed t test when α = 0.025 and n = 13?

2.179

What is the critical value for a two-tailed t test when α = 0.02 and n = 19?

2.552

Find the required χ2-value. For a χ2-curve with 10 degrees of freedom, find the χ2-value having area 0.99 to its right.

2.558

A research group wants to determine whether the proportion of car accidents caused by drivers using cell phones has changed from the previous value of 13%. They obtained 10,000 auto accident reports and found that 14% were caused by drivers using cell phones. The hypotheses are H0: p=0.13, Ha:p NOT =0.13 where p is the proportion of car accidents caused by drivers using cell phones.

2.974

At a certain university, the average cost of books was $400 per student last semester and the population standard deviation was $75. This semester a sample of 55 students revealed an average cost of books of $435 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?

3.46

A statistician claims that the standard deviation of the weights of firemen is more than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At α = 0.05, what is the critical value χ2 for this test?

30.144

A 90% confidence interval around the variance was calculated. For n= 27, the confidence interval was (35.0,88.4). Give the variance of the sample.

52 . 3

In a school district with 10,000 high school students, 1300 students completed a special class designed to improve their math skills. 780 of these scored better than the district-wide median on a standardized math exam. Does the special class have some value? The hypotheses are H0: p=0.5, Ha: p>0.5, where p is the proportion of all those taking the special class who score better than the district-wide median.

7.211

In a school district with 10,000 high school students, 1300 students completed a special class designed to improve their math skills. 780 of these scored better than the district-wide median on a standardized math exam. Does the special class have some value? The hypotheses are H0:p=0.5, Ha: p>0.5 where p is the proportion of all those taking the special class who score better than the district-wide median.

7.211

Quiz

7.4, 8.1, 8.2

Find the 90% confidence interval for the standard deviation of the lengths of pipes if a sample of 20 pipes has a standard deviation of 11 inches.

8.73 < σ < 15.07

A doctor believes that the standard deviation of systolic blood pressure is 450. A random sample of 24 patients found a standard deviation of 520. Assume the variable is normally distributed and α=0.01. What are the critical values?

9.262 and 44.181

A doctor claims that the standard deviation of systolic blood pressure is 12 mmHg. A random sample of 24 patients found a standard deviation of 14 mmHg. Assume the variable is normally distributed. At α = 0.01, what are the critical χ2 values?

9.262 and 44.181

Find the required χ2-value. For a χ2-curve with 3 degrees of freedom, find the χ2-value having area 0.025 to its right.

9.348

An average department store sells 150 men's suits per year. The men's suit departments at a particular national chain of stores claim that they sell more than the industry average. In a sample of 40 stores, they sold, on the average, 210 suits per year with a standard deviation of 40. What is the test value for this hypothesis?

9.49

Assume that a 90% confidence interval for the mean is (16.0, 19.0). Then a hypothesis test of H0: u = 17.0 at α= 0.10 would result in

Accepting the null hypothesis because 17.0 is between 16.0 and 19.0

The graph portrays the decision criterion for a hypothesis test for a population mean. The null hypothesis is The curve is the normal curve for the test statistic under the assumption that the null hypothesis is true. Use the graph to solve the problem. A graphical display of the decision criterion follows. https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/ESQ10_30416130855/f1q1g2.jpg Determine the nonrejection region.

All z-scores that lie to the right of -1.28

State whether the null hypothesis should be rejected on the basis of the given P-value. P-value = 0.242, o=0.05 , one-tailed test

Do not reject.

For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified. In the past, the mean running time for a certain type of flashlight battery has been The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: H0: μ = 8.3 hours Ha: μ > 8.3 hours Explain the meaning of a Type II error.

Failing to reject the hypothesis that μ = 8.3 hrs when in fact μ > 8.3 hrs

A right-tailed test is used when https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00016731d6531914c/f8q33-1.png

False

Sam Ying, a career counselor, claims the average number of years of schooling for an engineer is 15.8 years. A sample of 16 engineers had a mean of 15 years and a standard deviation of 1.5 years. The test value would be -2.68.

False

Sam Ying, a career counselor, claims the average number of years of schooling for an engineer is 15.8 years. A sample of 16 engineers had a mean of 15.0 years and a standard deviation of 1.5 years. The test value used in evaluating the claim would be -2.68.

False

Sandra Johnson, a researcher, believes her pulse rate will decrease with exercise. Her alternative hypothesis would contain an equal sign.

False

The χ2 critical value for n = 16 and α = 0.01 for a left-tailed test is 5.812.

False

The national average of times a person checks their email is 47.9 times per month. A random sample of 20 people yielded a mean of 31.1 email checks per month with a standard deviation of 4.5. At the 0.05 level of significance can it be concluded that this differs from the national average?

For a test value of -16.70, the P-value is < 0.05. Reject the null hypothesis.

Perform a hypothesis test for a population proportion using the critical value approach. A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 3%?

H0: p = 0.03 Ha: p > 0.03. Test statistic: z = 1.57. Critical value: z= 2.33 Fail to reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of defects exceeds 3%.

Perform a hypothesis test for a population proportion using the critical value approach. According to a recent poll the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 100 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use a 0.10 significance level.

H0: p = 0.53. H1: p ≠ 0.53. Test statistic: z = -1.60. Critical value: z= +/- 1.645 Fail to reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of people in New York who would vote for the incumbent president is different from 53%.

For the conjecture "The average weight of a cuckoo bird is less than 1.9 pounds", the null and alternative hypotheses are:

H0:The average weight of a cuckoo bird is equal to 1.9 pounds. H1: The average weight of a cuckoo bird is less than 1.9 pounds.

Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. A manufacturer claims that the mean amount of juice in its 16 oz bottles is 16.1 oz. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

Left-tailed

CH. 8-1

Lab/ HW

Ch. 8-2

Lab/ HW

Ch. 8-3

Lab/ HW

Ch. 8-4

Lab/ HW

Ch. 8-5

Lab/ HW

Ch. 8-6

Lab/ HW

Doctors nationally believe that 80% of a certain type of operation are successful. In a particular hospital, 47 of these operations were observed and 37 of them were successful. At α = .05, is this hospital's success rate different from the national average?

No, because the test value -0.22 is in the noncritical region.

Doctors nationally believe that 60% of a certain type of operation are successful. In a certain hospital, 51 of these operations were observed and 52% of them were successful. If α= .05, is this hospital's success rate different from the national average?

No, because the test value -1.17 is in the noncritical region.

A political strategist believes that 58% of voters in a certain state support his candidate. He then commissions a poll of 700 voters and 51% of them support his candidate. If α= .05, is the political strategist's belief warranted?

No, because the test value -3.75 is in the critical region.

A researcher knows from past studies that the standard deviation of the time it takes to inspect a house is 55 minutes. A sample of 24 houses is selected and inspected. The standard deviation was 45 minutes. At α= .01, can it be concluded that the standard deviation has changed?

No, comparing the test value 15.39 and the critical value.

A researcher claims that the standard deviation of the number of deaths annually from tornadoes in the U.S.A. is less than 30. If a sample of 9 randomly selected years had a standard deviation of 29, is the claim believable? Use α= .01?

No, comparing the test value 7.48 and the critical value 1.646.

Are the following statements H0: =7 and H1: Not =7 valid null and alternative hypotheses?

No, there are no parameters contained in these statements.

Are the following statements H0=7 and H1 NOT =7 valid null and alternative hypotheses?

No, there are no parameters contained in these statements.

s the statement H0: 16 = 8 a valid null hypothesis?

No, there is no parameter contained in this statement

Is the statement H0: 15=9 a valid null hypothesis?

No, there is no parameter contained in this statement.

Reginald Brown, an inspector from the Department of Weights and Measures, weighed 15 eighteen-ounce cereal boxes of corn flakes. He found their mean weight to be 17.8 ounces with a standard deviation of 0.4 ounces. At α = 0.01, are the cereal boxes lighter than they should be?

No. Critical value: -2.624 Test value: -1.94 Do not reject the Null hypothesis. There is not enough evidence to reject the claim that the cereal boxes weigh 18 ounces.

Science fiction novels average 310 pages in length. The average length of 10 randomly chosen novels written by I. M. Wordy was 325 pages in length with a standard deviation of 45. At = .05, are Wordy's novels significantly longer than the average science fiction novel?

No. Critical value: 1.833 Test value: 1.054 There is not enough evidence to support the claim that Wordy's novels are longer than the average science fiction novel.

Nationwide, the average salary of actuaries who achieve rank of Fellow is $150,000. An executive wants to see how this compares with Fellows within his company. In a sample of 8 Fellows the sample average is $155,800 with a standard deviation of $12,000. Can he/she conclude that Fellows in the company make more than the national average, using alpha=0.05?

No. Do not reject the null given t-value=1.3671 and P-value=0.1069 There is not enough evidence to support the claim that the Fellows earn more.

One of the assumptions for the chi-square test for a single variance is that the __________ must be normally distributed for the variable under study.

Population

Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. A national car insurance company stated that in 1987, the average yearly car insurance cost for a family in the U.S. was $1,716. In the same year, a random sample of 32 families in California resulted in a mean cost of . Does this suggest that the average insurance cost for a family in California in 1987 exceeded the national average? Perform the hypothesis test at a significance level of 10%. Assume that the population standard deviation is $35.50.

Reject H0. There is sufficient evidence to support the claim that the mean insurance cost for California drivers in 1987 exceeded the national average.

State whether the null hypothesis should be rejected on the basis of the given P-value. P-value = 0.021, o=0.05 , two-tailed test

Reject.

Assume that in a hypothesis test with null hypothesis H0: u= 14.0 at α=0.02, that a value of 11.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval result of

The 98% confidence interval for the mean contains the value 14.0

A political strategist claims that 56% of voters in Madison County support his candidate. In a poll of 100 randomly selected voters, 50 of them support the strategist's candidate. At α= .05, is the political strategist's claim warranted?

Yes, because the test value -1.21 is in the noncritical region.

Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29 with a standard deviation of five hours. A sample of 49 people had an average of 31 hours that they could go without sleep and still function normally. The test value for this hypothesis would be 2.8.

True

The critical chi-square value for 20 degrees of freedom for the figure below is 31.410. https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg0001063138eb33e48/q4-1.png

True

The critical value for a right-tailed test with α = 0.03 is 1.88.

True

When conducting a two-tailed -test with o=0.01 , the test value was 2.07. The decision would be: do not reject the null hypothesis.

True

A study claims that 60% of basketball injuries occur during games. A head trainer claims that this is too high for his team. His team had 16 injuries last season and only 5 occurred during games. Is his claim correct at α=0.05.

With a test value of -2.35, the P-value < 0.05. Reject the null hypothesis.

Educators claim that 75% of all high school students will attend college next fall. At Beechnut High School, with an enrollment of 818 seniors, a study found 645 will attend college in the fall. At α= 0.05, test the claim that at least 75% of all high school students will attend college in the fall. Use the P-value method.

With a test value of 2.54, the P-value < 0.05. Reject the null hypothesis.

Nationwide, the average waiting time until a electric utility customer service representative answers a call is 310 seconds. The Gigantic Kilowatt Energy Company randomly sampled 40 calls and found that, on average, they were answered in 281 seconds with a population standard deviation of 35 seconds. Can the company claim that they are faster than the average utility at α = 0.05?

Yes, because the test value -5.24 falls in the critical region.

A scientist claims that only 67% of geese in his area fly south for the winter. He tags 70 random geese in the summer and finds that 20 of them do not fly south in the winter. If α= .05, is the scientist's belief warranted?

Yes, because the test value 0.79 is in the noncritical region.

The average greyhound can reach a top speed of 18.6 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 45 of her dogs ran, on average, 19.0 meters per second with a population standard deviation of 1.4 meters per second. With α = 0.05, is her claim correct?

Yes, because the test value 1.92 falls in the critical region.

A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The target precision is a standard deviation of 1 mg/dL or less. If 18 measurements are taken and the standard deviation is 2 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at α= .01?

Yes, since the χ2 test value 68.000 is greater than the critical value 33.409.

A lumber mill is tested for consistency by measuring the variance of board thickness. The target accuracy is a variance of 0.0015 square inches or less. If 22 measurements are made and their variance is 0.005 square inches, is there enough evidence to reject the claim that the standard deviation is within the limit at α=.01?

Yes, since the χ2 test value 70.00 is greater than the critical value 38.932.

Is the statement H0: = 10 a valid null hypothesis?

Yes, this is a statement that compares a parameter to a value

For a random sample of 23 European countries, the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in all of Europe?

https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00016731d6531914c/f7q23-3.png

Which type of null hypothesis is used in the figure below? https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00016731d6531914c/f8q50-1.png

https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00016731d6531914c/f8q50-2.png

A garbage collector believes that he averages picking up more than four tons of garbage per day. What is the null hypothesis for his statement?

https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00016731d6531914c/f8q55-3.png

Which type of null hypothesis is used in the figure below?https://mycourses.utrgv.edu/courses/1/56533.201720/ppg/d6/brg00012cb138eb3373e/q9-1.png

null is backwards or simply = if a two tailed

You wish to test the claim that μ < 25.0 at the α = 0.05 significance level. In a sample of n = 53, the sample mean is 26.6. Assume that the population standard deviation, c, is 3. Compute the value of the test statistic.

z = 3.88

A recent study claims that business travelers spend an average of $41 per day on meals. A sample of 16 business travelers found that they had spent an average of $45 per day with a standard deviation of $3.65. If α=0.05 , what are the critical values?

± 2.131

A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05?

± 2.131

A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.04 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At, can you reject the claim that the machine is functioning properly? Justify your answer. (Assume that the variables are approximately normally distributed.) 11.98 11.91 11.96 11.94 12.03 12.01 11.97 12.06

χ2= 10.469, χ2 critical: 14.067; There is not enough evidence to reject the claim that the machine is working properly.