1.Suppose the pass rate in a subject used to be %50.

Then in one semester the midsemester test was replaced by an assignment

and in a sample of 145 students only 12 passed

what is the test stat for testing the claim the proportion is less than 50%?

2.Suppose you are the manager of a company that makes chocolate bars with and you want to test the claim

the population mean weight of the bars is above 200.

You get a sample of 194 bars that have an average weight of 200.64 g and standard deviation 0.17 g,

what is the test stat for testing the claim the mean weight is above 200?

3.Suppose in a sample of 400 apples79 are damagedYou want to test the claim the proportion that are defaceis lessthan 20%.

Hint There is strong evidence against H0 if the p-value is less than 0.05, alternatively there is strong evidence against H0 if the test stat is less than-1.645.

Which option is the correct hypothesis test?

Select one:

a.

H0: p= 0.8,H1 p> 0.8, standard error =10, test stat =0.5, p-value = 0.3084,reject H0 because there isstrong evidence the proprotion is above 80%

b.

H0: =0.2,H1: < 0.2, test stat =2.3, p-value = 0.01, do not reject H0 because there is not strong evidence the proprotion is above 80%

c.

H0: p= 0.2,H1 p <0.2, standard error =0.02test stat =-0.125, p-value = 0.4503, do not reject H0 because there is not strong evidence the proprotion is less than 20%

d.

H0: p> 0.8H1 p=0.8, test stat =-20 , p-value = 0.3084, do not reject H0 because there isstrong evidence the proprotion is above 80%

4. Suppose it is known that the standard deviation of the amount customers spend is $8.8

Also, suppose David and Susan both want to test the claim the average amount of money customers spend is less than$200 using a sample size of 100, they both get samples independently

In David's sample the mean is 192.3

In Sue's sample the mean is 185.8

Calculate the standard error and find the test stat for both David and Sue and answer the questions below

Some facts not in the course but discussed on youtube

David's probability valueisP(Z lessthan -8.75)

Sue's probability value is P(Z lessthan-16.136363636364)

a.The standard error is 0.88

b.Sue has more evidence that the mean is lessthan 200 so Sue's p-value will be lower than David's

c.Sue has more evidence that the mean is more than 200 so Sues p-value will be higherthan David's

d.David's test stat is -108.75

e.Sue's test stat is -16.14

5. Suppose that two researchers,

Researcher 1

and

Researcher 2

are both testing the claim the proportion of people that like a product is less than 0.28

Researcher 1 is going to use a sample size of1000 so the standard error of the sample proportion is

0.0142

Researcher 2 is going to use a sample size of 100 sostandard error of the sample proportion is

0.0449

In Researchers1 sampleof1000 people there are270 people thatlike the product

In Researchers 2sample of 100 people,27people thatlike the product

a.Researcher 1's test stat is -0.7043

b.Researcher 2'stest stat is -0.2227

c.Researcher 1 has more evidence the proportion is less than 0.28 than researcher 2, This means that Researcher 1 will have a lowerp-value than researcher 2

d.Researcher 1 has a probability value less than -1

6. You should use a webpage to find the test stat and pvalue for this question.

When you used the new machine to do100 tasks, the average time taken to complete each taskwas 9.7 minutes with a standard deviation 3

When you used the old machine to do100 tasks, the average time taken to complete each task was 16.9 minutes with a standard deviation 4

This is correct if you are testing the claim the average time the

the new machine takes to a task is different to the average time the new machine takes to do complete the task

Note that you use the webpage

http://www.usablestats.com/calcs/2samplet&summary=1;

to get the test statistics(the T stat is very similar to a zscore when n is large) and the p-value

a.

H0 1=2H1 1 2,test stat is 21.60, the p-value is less than 0.05, so do not reject H0

b.

H0 1=2H1 1 2,test stat is -14.40, the p-value isless than 0.05, so reject H0, there is strong evidence there is a difference between population means

c.

H0 1=2H1 1 2, test stat is 21.60, the p-value is less than 0.05, so reject H0, there is strong evidence that there is a difference between machines

d.

H0 1=2H1 1 2,test stat is -14.40, the p-value isless than 0.05, so do not reject H0