1. Suppose the length of25 bolts has an average of 120 with standard deviation of

35. Find a 95% confidence interval for the mean if 95% of sample means are within 2.064 estimated standard errors of the population mean when the sample size is 25

select the closest answer

a.

between 113.00 and 127.00

b.

between 825.55 and 854.45

c.

120

d.

35

e.

between 105.55 and 134.45

1. Suppose you have a sample of 1600 people and 804 people like the product.What is the

95% confidence interval for proportion if 95% of sample propoportions are within 1.96 standard errors of the population proportion.

a.

804.00

b.

between -0.02 and 0.03

c.

between 0.40 and 0.60

d.

between -0.48 and 1.48

e.

between 0.48 and 0.53

1. Supposethere is an opinion poll of 10,000 people and 7066 people support the politician

The estimate of the population proportion pis the sample proportion 7066/10000=0.7066

what is the standard error of this estimate ?

1. Suppose you get a sample of168 light bulbs and the mean life span is 403.2 days with standard deviation 9.3.

the sample mean 403.2 will be close to the population mean ,the standard error will tell you how close it usually is, what is the standard error of this estimate?

1. You need to use theautomatic dataset summarizerto find the p-value for

this question

Consider case 1

X. Y

1 18.9

1 21.1

2 38.9

2 41.1

Find the p-value for testing if there is a relationship between variables and select the correct option below

the test stat should be 12.856486930665

Also consider case 2

X Y

1 18.9

1 21.1

2 38.9

2 41.1

3 56.1

3 63.9

Find the p-value for testing if there is a relationship between variables and select the correct option below

the test stat should be 13.472519876849

Finally answer the question about p-value and sample size

a.

In case 1 the pvalue is -0.494004356

b.

as the sample size increases the p-value increases because there is more evidence

c.

in case 2 the p-value is 62.640175619

d.

in case 2 the p-value is 0.000175619

e.

In case 1 the pvalue is 0.005995644

f.

As the sample size increase the p-value decreases because there is more evidence

1. Be careful with this question, you must select both of the correct options given below

Use the followingdataset

And a filter to only select sample 12

Find the mean male BMI and the mean female BMI

click here for instructions

a.

The female mean BMI is 25.52

b.

The female mean BMI is 24.02

c.

The male mean BMI is 27.87

d.

The male mean BMI is 25.12

1. Suppose a market research firm has done some research on a product and has asked people if they would buy the product

would buy. won't buy total

old version4 96 100

new version16 84 100

For the old version the sample proportion that would buy the product

0.04 and the sample size is 100.

For the new version the sample proportion that would buy the product is0.16 and the sample size is 100.

find the p-value for testing the difference between the proportions by using thewebpage

http://epitools.ausvet.com.au/content.php?page=z-test-2

just enter the sample proportions and the sample sizes and click submit ,

select two sided test and use a desired significance level 0.05

click here for a guide that shows you how to use the webpage

After finding the p-value, check what happens to the p-value when you increase the sample size

also check what happens to p-value if you increase the difference between proportions

Be careful with question select all the correct options

a.

the pvalue is 4.4047

b.

the pvalue is 0.0047

c.

Increasing the difference in proporitions decreases the p-value

d.

If you keep the proportions the same but increase the sample size the p-value increases

e.

Increasing the difference in proporitions increases the p-value

f.

If you keep the proportions the same but increase the sample size the p-value decreases

1. Suppose a market research firm many people the question " how much would you pay for the product"

It does this for both the new version of the product and the old version of the product and obtains the following

results

sample averageSAMPLE

of amount they standard SAMPLE size

would pay deviation

old verison 20 3 100

new verison 20.7 4 100

use the webpage

https://www.medcalc.org/calc/comparison_of_means.php

to calculate the p-value for testing the difference between means

(this is the significance level p)

just enter the data click test.

Click here for a guide that shows you how to use the webpage to find p-value

After finding the p-value change the difference between the means and notice what happens to the p-value

alsoincrease the sample sizeand notice what happens to the p-value

alternatively you can use thep-value calculatorto find the p-value

click here for a guide to using the p-value calculator

be careful with this question answer all of the correct options

a.

the p-value is 0.1631

b.

If there is a larger difference between the means the p-value decreases

c.

If there is a larger difference between the means the p-value increases

d.

if the sample size increasesthe p-value decreases

e.

if the sample size increasesthe p-value increases

f.

the p-value is 6.4631

1. Tick all of the correct options (there is more than one correct option)

You will need to find pvalue using a webpage click here for a guide

For this question consider 2 cases

case 1

Consider the following sample

product 1 product 2 Product 3 total

male 6160 6200 6390 18750

female 6340 6300. 6110 18750

total 12500 12500 12500 37500

the chi square test stat is

9.664

case 2

product 1 product 2 Product 3 total

male 616 620 639 1875

female 634 630 611 1875

total 1250 1250 1250 3750

The chi square test statis0.9664

Note that the only difference between the cases is the sample sizes ,

the proportions are the same

In case 1

The sample proportions are 3 different numbers

phat1 =6160/12500=0.4928

,phat2 =6200/12500=0.496

phat3 = 6390/12500=0.5112

In case 2 the proportions are the same as case 1

phat1 =616/1250=0.4928

,phat2 =620/1250=0.496

phat3 = 639/1250=0.5112

a.

In both cases the difference in the proportionsis the same, however case 1 has a large sample size so it has more evidence the pvalue is higherfor case 1

b.

It would be better to do this question using a scatterplot because the variables are quantiative

c.

For case 2 the p-value is7.926806

d.

In both cases the difference in the proportionsis the same, however case 1 has a large sample size so it has more evidence, sothe pvalue is lower for case 1

e.

For case 1 the p-value is0.007971

f.

For case 2 the p-value is0.616806

g.

For case 1 the p-value is1.929971