1.

2.

3.

4.

5.

6.

H

OW MUCH SLEEP DID YOU GET LAST NIGHT

?

<6 6 7 8 9 >9

29% 14% 29% 14% 14% 0% 1 2 3 4 5 Slide 1- 1 6

S

LEEP AND

T

ECHNOLOGY     “43 percent of Americans say they rarely or never get a good night’s sleep during the week” “Nearly everyone, 95 percent, use electronics (like TV, computer, or cell phone) within the hour just before bed” “Researchers caution that the use of such devices are particularly harmful to the sleep-onset process, since the artificial light can suppress the release of melatonin which is our sleep hormone.” http://www.scientificamerican.com/podcast/episode.cfm

?id=electornic-gadgets-before-bed-can-h-11-03-07

C HAPTER 23 Inference About Means

A C ONFIDENCE I NTERVAL FOR M EANS ? ( CONT .)

One-sample t-interval for the mean

 When the conditions are met, we are ready to find the confidence interval for the population mean, μ.  The confidence interval is

y



t



n

 1   sample size.

SE y t

  

s n

confidence level, C, that you specify and on the number of degrees of freedom, n – 1, which we get from the

2. M ODEL  All models require assumptions, so state the assumptions and check any corresponding conditions.

     Assumptions you will test Independence Randomization 10% condition Normality  Determine Alpha Level

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HW-11 P

ROBLEM

5

 A nutrition lab test 50 ‘reduced sodium’ hot dogs, finding that the mean sodium content is 318mg with a standard deviation of 36mg.

 You want to create a 95% confidence interval to test your hypothesis.

 What assumptions have you made? Are these assumptions correct?

Slide 1- 6

8% 8% 83%

W

HAT ASSUMPTION HAVE WE MADE IN THIS INFERENCE

?

1.

2.

3.

We have assumed that the hot dogs weights are NOT multimodal and that the distribution of the population of hot dog weights does not contain any outliers.

We have assumed that the hot dog weights are random and that the distribution of the population of hot dog weights is not biased.

We have assumed that the hot dog weights are independent and that the distribution of the population of hot dogs is normal

Slide 1- 7

0% 17%

2.

3.

0%

4.

83%

“A

LAB TESTS

50

HOT DOGS

”. I

S THE RANDOMIZATION CONDITION SATISFIED

?

1.

No, because the hot dogs came from the same package No, there is evidence to believe that the hot dogs were not sampled at random Yes, there is definitely evidence to believe that the hot dogs were sampled at random We don’t know that the hot dogs were sampled at random, but it is reasonable to think that they were

Slide 1- 8

I

S THE

10%

CONDITION SATISFIED

?

1.

0%

2.

7%

3.

14%

4.

79%

No, 50 hot dogs are more than 10% of all hot dogs.

Yes, 50 hot dogs are more than 10% of all hot dogs.

No, 50 hot dogs are less than 10% of all hot dogs.

Yes, 50 hot dogs are less than 10% of all hot dogs.

Slide 1- 9

E

XPLAIN CLEARLY WHAT YOUR INTERVAL

7% 79% 7%

MEANS 1.

95% of the sodium content in this type of ‘reduced sodium’ hot dog will be contained in the interval 2.

3.

4.

We are 95% confident that the interval contains the true mean sodium content for this type of hot dog.

The interval contains the true mean sodium content in this type of ‘reduce sodium’ hot dogs 95% of the time.

95% of all ‘reduced sodium’ hot dogs will have a mean sodium content that falls within the interval

7% Slide 1- 10

HW 11 - P

ROBLEM

7

 Students investigating the packaging potato chips purchased 6 bags of chips from Kroger marked with a net weight of 28.1 grams.  They weighed the contents of each bag, recording the weight as follows:  29.2, 28.2, 29.1, 28.5, 28.8, 28.6

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I

S THE RANDOMIZATION CONDITION SATISFIED

?

1.

0%

We don’t know that the bag of chips were sampled at random, but it is reasonable to think that they were 2.

100%

No, the 6 bags were not selected at random, but it is reasonable to think that these bags are representative of the population 3.

0%

Yes, there is definitely evidence to believe that the bags of chips were sampled at random.

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I

S THE

10%

CONDITION SATISFIED

?

1.

0%

Yes, 6 bags of chips are more than 10% of the populations of all bags of chips 2.

100%

Yes, 6 bags of chips are less than 10% of the populations of all bags of chips 3.

0%

No, 6 bags of chips are more than 10% of the populations of all bags of chips 4.

0%

No, 6 bags of chips are less than 10% of the populations of all bags of chips

Slide 1- 13

D

ATA

: 29.2, 28.2, 29.1, 28.5, 28.8, 28.6

 Find the   Sample mean Sample standard deviation  Create  95% confidence interval for the mean weight

Slide 1- 14

T

HIS DATA IS ON THE WEIGHT OF A BAG OF POTATO CHIPS

. I

NTERPRET THE

95% CI

0%

1.

0%

2.

0%

3.

4.

100%

95% of all bags of chips will have a mean weight that falls within the interval 95% of the chips will be contained in the interval The interval contains the true mean weight of the contents of a bag of chips 95% of the time We are 95% confident that the interval contains the true mean weight of the contents of a bag of chips.

Slide 1- 15

C

OMMENT ON THE COMPANY

’

S STATE NET

28.1

G 1.

92%

Since the interval is ABOVE the stated weight of 28.1 grams, there is evidence that the company is filling the bags to MORE than the stated weight, ON AVERGAGE.

2.

8%

3.

0%

Since the interval is BELOW the stated weight of 28.1 grams, there is evidence that the company is filling the bags to LESS than the stated weight, ON AVERGAGE.

Since the interval CONTAINS the stated weight of 28.1 grams, there is evidence that the company is filling the bags to the stated weight, ON AVERGAGE.

Slide 1- 16

HW11- P

ROBLEM

10

 A company announced a ‘1000 Chips Trial’ claiming that every 18-ounce bag of its cookies contained at least 1,000 chocolate chips.  Students purchased random bags of cookies from different stores and counted the number of chips in each bag. Data were recorded to test the claim.

S

TUDENTS PURCHASED RANDOM BAGS OF COOKIES FROM DIFFERENT STORES

. I

S THE RANDOMIZATION CONDITION MET

100%

?

1.

2.

Yes No

1 0% Slide 1- 18 2

S

TUDENTS PURCHASED COOKIES FROM DIFFERENT STORES

. I

S THE INDEPENDENCE ASSUMPTION MET

?

1.

2.

Yes No

91% 1 9% 2 Slide 1- 19

I

S THE

10%

CONDITION MET

?

1.

2.

Yes No

100% 1 0% Slide 1- 20 2

I

S THE DATA NEARLY NORMAL

?

1.

2.

Yes No

100% 1 0% 2 Slide 1- 21

D

ATA 1022 1142 1120 1269 1276 1228 1202 1317 1325 1491

– C

REATE A

95% CI

Slide 1- 22

T

HE COMPANY CLAIMS AT LEAST

1000 C

HIPS IN

EVERY

BAG

. W

HAT WOULD YOU CONCLUDE

?

69%

1.

2.

3.

The company’s claim is true The company’s claim is false We cannot test this claim

31% 1 2 0% Slide 1- 23 3

HW 11 - P

ROBLEM 

9

One of the important factors in auto safety is the weight of the vehicle.

   Insurance companies are interested in knowing the average weight of cars currently licensed. They believe it is 3,000 lbs. (i.e. hypothesize).

To test this belief, they checked a random sample of 91 cars and found: Mean weight 2,855lbs.

  SD 531.5lbs

Is this strong evidence that the mean weight of all cars is NOT 3,000lbs.?

Slide 1- 24

I S THIS STRONG EVIDENCE THAT THE MEAN WEIGHT OF ALL CARS IS NOT 3000 LBS ?

0%

1.

0%

2.

0%

3.

4.

100%

Yes, there is sufficient evidence the mean is different from 3000 No, there is sufficient evidence the mean is different from 3000 Yes, there is NOT sufficient evidence the mean is different from 3000 No, there is NOT sufficient evidence the mean is different from 3000

Slide 1- 25

HW 11 -P

ROBLEM

11

Slide 1- 26

80% 0% 20% 0%

T EST THE HYPOTHESIS THAT THE MEAN COMPLETION TIME FOR THIS MAZE IS 60 SEC 1.

2.

3.

4.

Reject null, there is sufficient evidence to suggest the mean time is NOT 60 sec.

Reject null, there is NOT sufficient evidence to suggest the mean time is NOT 60 sec.

Fail to reject null, there is sufficient evidence to suggest the mean time is NOT 60 sec.

Fail to reject null, there is NOT sufficient evidence to suggest the mean time is NOT 60 sec.

Slide 1- 27

73% 0% 18% 9%

E

LIMINATE THE OUTLIER THEN

,

TEST THE HYPOTHESIS THAT THE MEAN COMPLETION TIME FOR THIS MAZE IS

60

SEC 1.

2.

3.

4.

Reject null, there is sufficient evidence to suggest the mean time is NOT 60 sec.

Reject null, there is NOT sufficient evidence to suggest the mean time is NOT 60 sec.

Fail to reject null, there is sufficient evidence to suggest the mean time is NOT 60 sec.

Fail to reject null, there is NOT sufficient evidence to suggest the mean time is NOT 60 sec.

Slide 1- 28

D

O YOU THINK

THIS

MAZE MEETS THE 1.

0%

“

ONE

-

MINUTE AVERAGE

”

REQUIREMENT

?

There is NOT evidence that the mean time required for rats to complete the maze is different from 60s. The maze meets the requirements.

2.

10%

There is evidence that the mean time required for rats to complete the maze is different from 60s. The maze meets the requirements.

3.

90%

There is evidence that the mean time required for rats to complete the maze is different from 60s. The maze DOES NOT meet the requirements.

4.

0%

There is NOT evidence that the mean time required for rats to complete the maze is different from 60s. The maze DOES NOT meet the requirements.

Slide 1- 29

U

PCOMING IN

C

LASS  Homework #11 due Monday  Start working on the final step of your data project  Quiz #6 next Thursday  Exam #2 is Thursday April 26 th .

Slide 1- 30