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Week 5 : Hypothesis Testing II: One Sample Hypothesis Tests - Checkpoint

1. Complete Exercise 9.13 (The Video Game Satisfaction Case) on page 357 in your textbook 9.13: THE VIDEO GAME SATISFACTION RATING CASE VideoGame

Recall that very satisfied customers give the XYZ-Box video game system a rating that is a a: b:

Letting represent the mean composite satisfaction rating for the XYZ-Box, set up th

The random sample of 65 satisfaction ratings yields a sample mean of x = 42.954. A

c: Using the information in part b, calculate the p-value and use it to test H0 versus Ha (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti

9.13 a. b. c. H0 : 42 versus Ha : > 42

z = 2.91. Since this exceeds the critical values 1.28, 1.645, and 2.33, can reject H0 a p- value = .0018. Same conclusion as part (b)

d. Very strong (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti

Checkpoint

on page 357 in your textbook. (Points : 7)

game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use

ting for the XYZ-Box, set up the null hypothesis H0 and the alternative hypothesis Ha needed if we wis

ample mean of x = 42.954. Assuming that s equals 2.64, use critical values to test H0 versus Ha at e

nd use it to test H0 versus Ha at each of = .10, .05, .01, and .001. d How much evidence is there tha n. McGraw-Hill Learning Solutions, 2012. p. 357).

645, and 2.33, can reject H0 at = .1, .05, and .01. Fail to reject H0 at = .001

n. McGraw-Hill Learning Solutions, 2012. p. 653).

e XYZ-Box wishes to use the random sample of 65 satisfaction ratings to provide evidence supporting

hesis Ha needed if we wish to attempt to provide evidence supporting the claim that exceeds 42.

to test H0 versus Ha at each of = .10, .05, .01, and .001.

uch evidence is there that the mean composite satisfaction rating exceeds 42?

vide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceed

m that exceeds 42.

g for the XYZ-Box exceeds 42.

2 2. Complete Exercise 9.19 on page 358 in your textbook. (Points : 7) 9.19: The Crown Bottling Company has just installed a new bottling process that will f a: The bottling company wants to set up a hypothesis test so that the filler will be

b: Suppose that Crown Bottling Company decides to use a level of significance of (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti a. H0 : = 16 versus Ha : 16

b. z = 3.00, p-value = .0027, critical values 2.575, [16.007, 16.093], reject H0 an (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti

ottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfillin

t so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hy

a level of significance of = .01, and suppose a random sample of 36 bottle fills is obtained from a tes Graw-Hill Learning Solutions, 2012. p. 358).

007, 16.093], reject H0 and decide to readjust; z = 2.40, p-value = .0164, 2.575, [15.917, 16.003], Graw-Hill Learning Solutions, 2012. p. 654).

a soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer com

he null and alternative hypotheses for this hypothesis test.

lls is obtained from a test run of the filler. For each of the following four sample means x=16.05, x

2.575, [15.917, 16.003], fail to reject H0 so dont readjust, z = 1.20, p-value = .2302, 2.575, [15.97

ng leads to customer complaints and overfilling costs the company considerable money. In order to ve

le means x=16.05, x=15.96, x=16.02, and x=15.94 determine whether the fillers initial setup

= .2302, 2.575, [15.977, 16.063], fail to reject H0 so dont readjust; z = 3.60, p-value = .00032,

ble money. In order to verify that the filler is set up correctly, the company wishes to see whether the

er the fillers initial setup should be readjusted. In each case, use a critical value, a p-value, and a con

3.60, p-value = .00032, 2.575, [15.897, 15.983], reject H0 so and decide to readjust

shes to see whether the mean bottle fill, , is close to the target fill of 16 ounces. To this end, a rando

lue, a p-value, and a confidence interval. Assume that s equals .1.

ces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If t

put of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that

bt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the fillers initial setup will

e fillers initial setup will be readjusted.

9.29

3. Complete Exercise 9.29 (The Video Game Satisfaction Rating Case) on page 362 in your te 9.29: THE VIDEO GAME SATISFACTION RATING CASE VideoGame

Recall that very satisfied customers give the XYZ-Box video game system a composite sati a: Letting represent the mean composite satisfaction rating for the XYZ-Box, set

The mean and the standard deviation of a sample of n = 65 customer satisfaction ratings are (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti a. H0 : 42 versus Ha > 42

b. t = 2.90 > 2.386, so reject H0 and decide > 42. Since the p- value = .0026, w (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti

e) on page 362 in your textbook. (Points : 7)

system a composite satisfaction rating that is at least 42.

ting for the XYZ-Box, set up the null and alternative hypotheses needed if we wish to attempt to provid

er satisfaction ratings are x=42.95 and s = 2.6424. Use a critical value to test the hypotheses you se Graw-Hill Learning Solutions, 2012. p. 362).

e the p- value = .0026, we have very strong evidence that 42. Graw-Hill Learning Solutions, 2012. p. 654).

wish to attempt to provide evidence supporting the claim that exceeds 42.

st the hypotheses you set up in part by setting equal to .01. Also, interpret the p-value of .0025 for

t the p-value of .0025 for the test.

4. Complete Exercise 9.31 on page 362 in your textbook. (Points : 7) 9.31: a:

Consider a chemical company that wishes to determine whether a new catalyst,

Letting be the mean of all possible yields using the new catalyst, set up the nu

b: The mean and the standard deviation of the sample of 5 catalyst yields are x= (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti a. H0 : = 750 versus Ha : 750

b. t = 6.94 > 4.604; reject H0. Since the p- value < .01, we have very strong evide (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti

e whether a new catalyst, catalyst XA-100, changes the mean hourly yield of its chemical process from

ew catalyst, set up the null and alternative hypotheses needed if we wish to attempt to provide eviden

5 catalyst yields are x=811 and s = 19.647. Using a critical value and assuming approximate normal Graw-Hill Learning Solutions, 2012. pp. 362 - 363).

we have very strong evidence that 750. Graw-Hill Learning Solutions, 2012. p. 654).

ts chemical process from the historical process mean of 750 pounds per hour. When five trial runs are

attempt to provide evidence that differs from 750 pounds.

ming approximate normality, test the hypotheses you set up in part by setting equal to .01. The p-v

. When five trial runs are made using the new catalyst, the following yields (in pounds per hour) are re

ng equal to .01. The p-value for the hypothesis test is given in the Excel output on the page margin.

n pounds per hour) are recorded: 801, 814, 784, 836, and 820. ChemYield

put on the page margin. Interpret this p-value.

5. Complete Exercise 9.42 on page 367 in your textbook. (Points : 7) 9.42: a.: b.: The manufacturer of the ColorSmart-5000 television set claims that 95 percent

Letting p be the proportion of ColorSmart-5000 television sets that last five year

Use critical values and the previously given sample information to test the hypo

c.: Do you think the results of the consumer groups survey have practical importan (Bowerman, Bruce.. Essentials of Business Statistics, 4th Edition. McGraw-Hill Learning Soluti a.b.

: p = .95 versus : p < .95.

Reject at each value of ; extremely strong evidence. c. Probably, is far below the claimed .95. LO1, LO5

t claims that 95 percent of its sets last at least five years without needing a single repair. In order to te

on sets that last five years without a single repair, set up the null and alternative hypotheses that the

ormation to test the hypotheses you set up in part by setting equal to .10, .05, .01, and .001. How

y have practical importance? Explain your opinion. Graw-Hill Learning Solutions, 2012. pp. 367 - 368).

, is far below the claimed .95.

ingle repair. In order to test this claim, a consumer group randomly selects 400 consumers who have o

tive hypotheses that the consumer group should use to attempt to show that the manufacturers claim .05, .01, and .001. How much evidence is there that the manufacturers claim is false?

00 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consume

the manufacturers claim is false.

m is false?

s. Of these 400 consumers, 316 say that their ColorSmart-5000 television sets did not need repair, wh

s did not need repair, while 84 say that their ColorSmart-5000 television sets did need at least one rep

did need at least one repair.