Determine the null hypothesis and the alternate hypothesis:|Mathematics – Statistics

Determine the null hypothesis and the alternate hypothesis:|Mathematics – Statistics

A group  of cognitive psychologists studying the effects of sleep deprivation on short-term memory decay had eight participants stay in a sleep lab for two days. Four participants were randomly assigned to a condition in which they were not permitted to sleep during that period, while the other four participants were allowed to sleep when they wanted to. At the end of the two days, the participants completed a short-term memory task that yielded the results in the table that follows.

Mean Number of Letters Remembered

Sleep Deprived

Normal Sleep

7

9

8

8

7

11

9

7

applying  the .05 significance level, did sleep deprivation reduce short-term memory?

Choose the correct HO and HA statements:

Problem# 1 options:

A)

HO : μdeprived = μnormal

HA : μdeprived > μnormal

B)

HO : μdeprived = μnormal

HA : μdeprived < μnormal

C)

HO : pdeprived = pnormal

HA : pdeprived < pnormal

D)

HO : μdeprived = μnormal

HA : μdeprived ≠ μnormal

Problem# 2

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the most appropriate hypothesis test to use for the following scenario:

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A group  of cognitive psychologists studying the effects of sleep deprivation on short-term memory decay had eight participants stay in a sleep lab for two days. Four participants were randomly assigned to a condition in which they were not permitted to sleep during that period, while the other four participants were allowed to sleep when they wanted to. At the end of the two days, the participants completed a short-term memory task that yielded the results in the table that follows.

Mean Number of Letters Remembered

Sleep Deprived

Normal Sleep

7

9

8

8

7

11

9

7

Using the .05 significance level, did sleep deprivation reduce short-term memory?

The most appropriate hypothesis test to use for this scenario is:

Problem# 2 options:

A)

t – test for dependent means

B)

t – test for independent means

C)

Χ2 test for independence

D)

two-population proportion t-test

E)

z – test for two population means

Problem# 3

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the null hypothesis and the alternate hypothesis:

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A B2B Marketing Insider blog of October 7, 2010 examined five currently-used sales closing techniques. Sales scenarios are presented to a sample of 230 purchasing executives. Each subject received one of the five closing techniques or a scenario in which no sales close was achieved. After reading the sales scenario, each executive was asked to rate his/her level of trust in the salesperson on a 7-point scale. The following table reports the six treatments employed in the study and the number of subjects receiving each treatment:

Treatments: Sales Closing Technique

Sample Size

No Close

35

Financial close

35

Time Line close

30

Sympathy close

40

The Visual close

35

Thermometer close

55

(Source: Based on Hawes, J.M. “Do Closing Techniques Diminish Prospect Trust?” from Industrial Marketing Management, September 1996, Volume 25(5))

Is the salesperson’s level of trust influenced by the choice of closing method? Test at 5% significance level.

Choose the correct HO and HA statements:

Problem# 3 options:

A)

HO : p1 = p2 = p3 = p4 = p5 = p6

HA : At least two proportions are different

B)

HO : μ1 = μ2 = μ3 = μ4 = μ5 = μ6

HA : At least two population means are different

C)

HO : μ1 = μ2

HA : μ1 ≠ μ2

D)

HO : μ1 = μ2 = μ3 = μ4 = μ5 = μ6

HA : At least three population means are different

Problem# 4

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the most appropriate hypothesis test to use for the following scenario:

**************************

A B2B Marketing Insider blog of October 7, 2010 examined five currently-used sales closing techniques. Sales scenarios are presented to a sample of 230 purchasing executives. Each subject received one of the five closing techniques or a scenario in which no sales close was achieved. After reading the sales scenario, each executive was asked to rate his/her level of trust in the salesperson on a 7-point scale. The following table reports the six treatments employed in the study and the number of subjects receiving each treatment:

Treatments: Sales Closing Technique

Sample Size

No Close

35

Financial close

35

Time Line close

30

Sympathy close

40

The Visual close

35

Thermometer close

55

(Source: Based on Hawes, J.M. “Do Closing Techniques Diminish Prospect Trust?” from Industrial Marketing Management, September 1996, Volume 25(5))

Is the salesperson’s level of trust influenced by the choice of closing method? Test at 5% significance level.

The most appropriate hypothesis test to use for this scenario is:

Problem 4 options:

A)

two-population proportion z-test

B)

t – test for independent means

C)

one-way ANOVA

D)

Χ2 test for goodness of fit

E)

t – test for single population mean

Problem# 5

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the null hypothesis and the alternate hypothesis:

*************************

An experimenter conducted a study of the relation of size in a particular species of bird to behavioral displays of dominance. The results for the first four birds observed were as follows.

Bird Size

Bird Behavior (Displays of Dominance)

14

74

18

82

14

74

10

70

Using α = 0.05, is the relation of size to behavioral display statistically significant?

Choose the correct HO and HA statements:

Problem 5 options:

A)

HO : p1 = p2

HA : p1 ≠ p2

B)

HO : r = 0

HA : r ≠ 0

C)

HO : linear relationship is not statistically significant (population correlation coefficient = 0)

HA : linear relationship is statistically significant (population correlation coefficient ≠ 0)

D)

HO : μ1 = μ2

HA : μ1 ≠ μ2

Problem 6

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the most appropriate hypothesis test to use for the following scenario:

**************************

An experimenter conducted a study of the relation of size in a particular species of bird to behavioral displays of dominance. The results for the first four birds observed were as follows.

Bird Size

Bird Behavior (Displays of Dominance)

14

74

18

82

14

74

10

70

Using α = 0.05, is the relation of size to behavioral display statistically significant?

The most appropriate hypothesis test to use for this scenario is:

Problem 6 options:

A)

z – test for two population proportion

B)

t – test for independent means

C)

t – test for dependent means

D)

t – test for significance of correlation coefficient r

E)

Χ2 test for independence

Question 7 (0.4 points)

One of the most difficult things to do in statistics is to determine the correct hypothesis test to do for a given scenario.

Determine the null hypothesis and the alternate hypothesis:

**************************

Each year, Kiplinger’s compiles its list of Best Value Cities. One of the statistics used in this ranking is the cost-of-living index compiled by the US Department of Labor Bureau of Labor Statistics. The index measures the cost of living in a city relative to the national average of 100. In 2011, Pueblo Colorado had the lowest index (84), while New York City had an index of 118. The following table lists the cost of living for seven Southeastern US cities:

City

Cost of Living Index (US mean = 100)

Charlotte, NC

93.0

Birmingham, AL

89.6

Florence, SC

100.0

Tampa, FL

92.1

Atlanta, GA

95.2

Knoxville, TN

89.7

Miami, FL

107.7

Is the true mean cost of living index for Southeastern US cities lower than the national mean cost-of-living index of 100? Test at 2% significance level.

Choose the correct HO and HA statements:

Problem 7 options:

A)

HO : μSoutheast = μNational

HA : μSoutheast < μNational

B)

HO : μSoutheast = μNational

HA : μSoutheast ≠ μNational

C)

HO : pSoutheast = pNational

HA : pSoutheast ≠ pNational

D)

HO : μSoutheast = μNational

HA : μSoutheast > μNational

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