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statistics alive

Questions and Answers of Statistics Alive

calculate the sample variance, s2. Construct a 95% confidence interval for the population variance, σ2 . Test the given hypothesis using a =.05. 9. n = 7: 1.4, 3.6, 1.7, 2.0, 3.3, 2.8, 2.9 to test
Use the information given to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom 11. F 2.85, df = 8, df =16
1. Under what assumptions can the F distribution be used in making inferences about the ratio of the population variances?
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. 2. n, 3, n, 8, a = .050 =3, =
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. 3. n, 7, n=5, a = .010
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. == 4. n, 13, n, 14, a=.100
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. 5. n, 16, n, 19, a = .005 =19,
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. 6. n =25, n=26, a = .050
Find the tabled value for an F variable based on n1 - 1 numerator degrees of freedom, n2 - 1 denominator degrees of freedom with an area of a to its right. 7. n, 10, n, 10, a = .025 "
Use the information given to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom 8. F=8.36, df = 5, df =4
Use the information given to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom 9. F 6.16, df = 4, df = 13
Use the information given to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom 10. F 1.62, df = 15, df = 25
The variability in the amount of impurities in a batch of chemical depends on the length of its process time. A manufacturer using two production lines, 1 and 2, has made a slight adjustment to line
An experimenter is concerned that the variability of responses using two different procedures may not be the same. Before conducting his research, he conducts a prestudy with random samples of 10 and
calculate the sample variance, s2. Construct a 95% confidence interval for the population variance, σ2 . Test the given hypothesis using a =.05. 10. n 10: 18.9, 9.7, 12.0, 8.7, 10.6, 8.9, 7.2,
11. Cerebral Blood Flow Cerebral blood flow (CBF)in the brains of healthy people is normally distributed with a mean of 74. A random sample of 25 stroke patients resulted in an average CBF of 69.7
12. A Precise Quarterback The number of passes completed and the total number of passing yards recorded for the Los Angeles Chargers quarterback, Philip Rivers for each of the 15 regular season games
13. Instrument Precision A precision instrument is guaranteed to read accurately to within 2 units. A sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and
14. Pollution Control The EPA limit on the allowable discharge of suspended solids into rivers and streams is 60 milligrams per liter (mg/L) per day. A study of water samples selected from the
15. Drug Potency To properly treat patients, drugs prescribed by physicians must have not only a mean potency value as specified on the drug’s container, but also small variation in potency values.
16. Drug Potency, continued Refer to Exercise 15.Testing of 60 additional randomly selected containers of the drug gave a sample mean and variance equal to 5.04 and .0063 (for the total of n564
17. Hard Hats A manufacturer of hard safety hats for construction workers wants the mean force transmitted by helmets to be 3200 newtons (or less), well under the legal 4000-newton limit, and  to
18. Hard Hats, continued Refer to Exercise 17. Do the data provide sufficient evidence to indicate that exceeds 160?
19. Light Bulbs A manufacturer of industrial light bulbs wants the bulbs to have a mean length of life that is acceptable to its customers and a variation in length of life that is relatively small.
Check your ability to use Table 6 in Appendix I by verifying the following statements:1. The value of F with area .05 to its right for 6 1 df 5 and df 59 is 3.37 2 .2. The value of F with area .05 to
15. Lead Levels in Drinking Water Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following information on lead levels (in parts per million):a.
29. What’s Normal? What is normal, when it comes to people’s body temperatures? A random sample of 130 human body temperatures, provided by Allen Shoemaker4 in the Journal of Statistical
28. Biomass Studies indicate that the biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m2 ), may in fact be too high and that tropical biomass values vary
27. Acidity in Rainfall Refer to Exercise 30 (Section 8.3)and the collection of water samples to estimate the mean acidity (in pH) of rainfalls. Remember that the pH for pure rain falling through
26. Flextime A company wants to implement a flextime schedule so that workers can schedule their own work hours, but it needs a minimum mean of 7 hours per day per assembly worker in order to operate
25. Potency of an Antibiotic A drug manufacturer claimed that the mean potency of one of its antibiotics was 80%. A random sample of n5100 capsules was tested and produced a sample mean of x 579.7%
24. O Baby! The weights of 3-month-old baby girls are known to have a mean of 5.86 kilograms.2 Doctors at an inner city pediatric facility suspect that the average weight of 3-month-old baby girls at
23. Hamburger Meat Ground beef is packaged in small trays, intended to hold 1 pound of meat. A random sample of 35 packages in the small tray produced weight measurements with an average of 1.01
22. Airline Occupancy Rates Suppose a scheduled airline flight must average at least 60% occupancy in order to be profitable. Occupancy rates were recorded daily for a regularly scheduled flight on
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
30. Sports and Achilles Tendon Injuries Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study in The American
31. Hybrid or EV? In an attempt to reduce their carbon footprint, many consumers are purchasing hybrid, plug-in hybrid, or electric cars. Consumer Reports ranks the Chevrolet Bolt first among
To determine whether car ownership affects a student’s academic achievement, random samples of 100 car owners and 100 nonowners were drawn from the student body. The grade point average for the 100
14. Healthy Eating Has the consumption of red meat decreased over the last 10 years? A researcher selected hospital nutrition records for 400 subjects surveyed 10 years ago and compared the average
13. Cure for the Common Cold? An experiment was planned to compare the mean time (in days) to recover from a common cold for people given a daily dose of 4 milligrams (mg) of vitamin C versus those
12. Losing Weight In a comparison of the mean 1-month weight losses for women aged 20–30 years, these sample data were obtained for each of two diets:Do the data provide sufficient evidence to
11. Spraying Fruit Trees A fruit grower wants to test a new spray that a manufacturer claims will reduce the loss due to insect damage. To test the claim, the grower sprays 200 trees with the new
10. Put on the Brakes The braking ability was compared for two 2018 automobile models. Random samples of 64 automobiles were tested for each type. The recorded measurement was the distance (in
9. Breaking Strengths of Cables A test of the breaking strengths of two different types of cables was conducted using samples of 100 1 2 n 5n 5 pieces of each type of cable.Do the data provide
8. Using the p-value approach for the data in Exercise 6, is there sufficient evidence to show that 1 m is larger than 2 m at the 1% level of significance? Is this result consistent with the results
7. Using the p-value approach for the data in Exercise 5, is there sufficient evidence to show that 1 m is larger than 2 m at the 1% level of significance? Is this result consistent with the results
More Hypothesis Tests Independent random samples were selected from two quantitative populations, with sample data given . If your research objective is to show that 1 m is larger than 2 m , use the
More Hypothesis Tests Independent random samples were selected from two quantitative populations, with sample data given . If your research objective is to show that 1 m is larger than 2 m , use the
4. Calculate the p-value for the data in Exercise 2.Use the p-value to test for a significant difference in the population means at the 5% significance level.
3. Calculate the p-value for the data in Exercise 1.Use the p-value to test for a significant difference in the population means at the 5% significance level.
Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given State the null and alternative hypotheses used to test for a difference in
Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given State the null and alternative hypotheses used to test for a difference in
Construct a 95% confidence interval for the difference in average academic achievements between car owners and nonowners. Using the confidence interval, can you conclude that there is a difference in
A random sample of n535 observations from a quantitative population produced a mean x 52.4 and a standard deviation of s5.29. Your research objective is to show that the population mean m exceeds
Find the p-values for the z-tests and determine the significance of the results. 13. A left-tailed test with observed z=-1.81
14. Calculate the value of the z-statistic based on the sample mean, x . Is this an unusual value of z? It is reported1 that the average or mean number of Facebook friends is 155. Suppose that when
13. If we were looking to dispute the reported average of 155, how would you express 0 H and a H ? It is reported1 that the average or mean number of Facebook friends is 155. Suppose that when 50
12. What is the probability of observing a value of z53.51 or greater if 0 H is true? What might you conclude? A new variety of pearl millet is expected to provide an increased yield over the variety
11. Find the value of the test statistic for testing the hypotheses that the new variety will increase yield. Is the value of the test statistic likely, assuming 0 H is true? A new variety of pearl
10. A seed wash is expected to change the proportion p of seeds that germinate when planted in poorlydraining soil. Suppose that the current germination rate is about 80%. state the null and
9. The new tax structure is supposed to help small businesses survive. Suppose we know that presently 20% of all small businesses fail in their first year. state the null and alternative hypotheses
8. A new variety of pearl millet is expected to provide an increased yield over the variety presently in use, which has a mean yield of about 70 bushels per acre. state the null and alternative
7. A researcher wishes to show that a modified treatment decreases the mean time to recovery m, which is currently 5 days. state the null and alternative hypotheses to be tested.
6. A researcher claims that a binomial proportion p is at least 0.8. A statistical test is designed to disprove the researcher’s claim. state the null hypothesis, H0, and the alternative
5. A statistical test is designed to show that the mean m is different from 100. state the null hypothesis, H0, and the alternative hypothesis, Ha , to be tested.
4. A statistical test is designed to show that the proportion p of defectives has decreased below 0.5%. state the null hypothesis, H0, and the alternative hypothesis, Ha , to be tested.
3. A statistical test is designed to show that the mean m is greater than 3.state the null hypothesis, H0, and the alternative hypothesis, Ha , to be tested.
2. Define the level of significance
1. List the five parts of a statistical test.
A die cutting process for sheet metal currently produces an average of 3% defectives. You are interested in showing that a simple adjustment on a machine will decrease p, the proportion of defectives
15. What is the probability of observing a value of z greater than 1.43 or less than 21.43? What might you conclude about the average number of Facebook friends? It is reported1 that the average or
The average weekly earnings for female social workers is $670. Do men in the same positions have average weekly earnings that are higher than those for women? A random sample of n540 male social
The daily yield for a local chemical plant has averaged 880 tons for the last several years.The quality control manager would like to know whether this average has changed in recent months. She
Find the p-values for the z-tests and determine the significance of the results. 12. A two-tailed test with observed z=-2.78.
Find the p-values for the z-tests and determine the significance of the results. 11. A right-tailed test with observed z=1.15.
For the situations described find the appropriate rejection regions and state your conclusion if the observed test statistic was z522.41. If appropriate, provide a measure of reliability for your
For the situations described find the appropriate rejection regions and state your conclusion if the observed test statistic was z522.41. If appropriate, provide a measure of reliability for your
For the situations described find the appropriate rejection regions and state your conclusion if the observed test statistic was z522.41. If appropriate, provide a measure of reliability for your
Find the appropriate rejection regions and state your conclusion if the observed test statistic was z=-.16.If appropriate, provide a measure of reliability for your conclusion 7. A two-tailed test
Find the appropriate rejection regions and state your conclusion if the observed test statistic was z=-.16.If appropriate, provide a measure of reliability for your conclusion 6. A right-tailed test
5. What is the power of a test and how is it related to b?
4. What is the p-value for a test of hypothesis?
3. For a fixed value of , what is the effect on b when the sample size is increased?
2. For a fixed sample size n, what is the effect on b when  is decreased?
1. Define  and b for a statistical test of hypothesis.
Refer to Example 9.5. Calculate b and the power of the test (12b) when m is actually equal to 870 tons.
Standards set by government agencies indicate that Americans should not exceed an average daily sodium intake of 3300 milligrams (mg). To find out whether Americans are exceeding this limit, a sample
Refer to Example 9.5. The quality control manager wants to know whether the daily yield at a local chemical plant—which has averaged 880 tons for the last several years—has changed in recent
You wish to show that the average hourly wage of electricians in the state of California is different from $21, which is the national average. This is the alternative hypothesis, written as H :m ?21
3. Can you think of some possible reasons why the results of these two studies, which were alike in some respects, produced such different conclusions? On Wednesday, January 27, 1988, the front page
1. Bass Fishing The pH factor is a measure of the acidity or alkalinity of water. A fishing expert states that the best chance of catching bass occurs when the pH of the water is between 7.5 and
Use the data from Example 8.11 involving citizens opinions about a bond proposal, reproduced as follows. Is there evidence of a difference in the proportions favoring the proposal for the two
Use the data from Example 8.11 involving citizens opinions about a bond proposal, reproduced here.Suppose that the citizens in the developing section of the city have no opinion about this proposal,
The tire wear of n1 5 n2 5 100 tires of two types in Example 8.9 had sample means and standard deviations shown in the table. Is there evidence of a difference in the tire wear for the two types of
The random sample of n 5 100 Americans in Example 9.7 had an average of 3400 mg of sodium per day, with a sample standard deviation of 1100 mg. Does this provide sufficient evidence to indicate that

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