MAT220 STATISTICS

Assignment 2

Due April 21, 2017

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Instructions

·     Show all relevant workings

·     Up to 10 points will be deducted for untidy work

·     A cover page must be attached showing the order in which questions were answered

·     Where appropriate, include the graph of the normal distribution curve to aid in answering questions

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1.    Cans of lemonade are filled by a machine which is set to dispense an amount which is normally distributed with mean 330ml and standard deviation 2.4ml. A quality control manager suspects that the machine is over-dispensing and tests a random sample of 8 cans.

                    The volume of the contents, in ml, are as follows:

                       329   327   331   326   334    343    328    339

        Test at the 2 % significance level, whether the manager’s suspicion is justified.

 

 

 

 

2.    A drug company tested a new pain-relieving drug on a random sample of 100 headaches sufferers. Of these, 75% said that their headache was relieved by the drug. With the currently marketed drug, 65% of users say that their headaches were relieved by it. Test at the 4% level, whether the new drug will have a great proportion of satisfied users.

 

 

 

 

 

 

3.    A food processor produces large quantities of jars of Jam. In each batch, the gross weight of a jar is known to be normally distributed with standard deviation 7.5g. (The gross weight is the weight of the jar plus the weight of the jam.)

                 The gross weights, in grams, of a random sample from a particular batch were:

514

485

501

486

502

496

509

491

497

501

506

486

498

490

484

494

501

506

490

487

507

496

505

498

499

                          

 

 

 

a.   Estimate the proportion of this batch with gross weight over 500g. Calculate an approximate 95% confidence interval for this proportion

b.  Calculate a 905confidence interval for the mean gross weight of this batch.

 

 

 

 

 

4.    A croupier at a casino is accused of using a die which is biased towards showing a six. The management tests the die by rolling it 500 times, and 98 sixes were recorded. At the 5% significance level, does this result support the compliant?

To try to eliminate complaints, a new die is suggested. This die is also rolled 500 times, and 90 sixes were recorded.

a.    Calculate a 99% confidence interval for the proportions of sixes the die will show.

b.    At a 5% significance level, does this die show bias towards a six?

 

 

 

 

5.    A study of seat belt users and non-users yielded the randomly selected sample data summarized in the given table. Test the claim that the amount of smoking is independent of seatbelt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seatbelts. Is this theory supported by the sample data?

 

Number of cigarettes smoked per day

 

0 day

1-14 days

15-34 days

35 and over days

Wear seatbelts

175

20

42

6

Doesn’t wear seatbelts

149

17

41

9

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