1. Use the Chi Square Distribution Table to find the following critical 22 values.

Chi Square Distribution Table

a. 20.02520.025 for df=4df=4

b. 20.120.1 for df=6df=6

c. 20.9520.95 for df=7df=7

2. A dentist wondered if his appointments were distributed evenly from Monday to Friday each week. He took a random sample of 500 appointments and recorded which day of the week they were booked for. His results are:

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Appointment Frequency	99	119	118	93	71

The dentist would like to use these results to conduct a 22 goodness-of-fit test to determine if the distribution of appointments agrees with an even distribution using a 5% level of significance.

Chi Square Distribution Table

a. Calculate the test statistic.

2=2=

Round to two decimal places if necessary

b. Determine the critical value(s) for the hypothesis test.

• +

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

3. A psychologist is interested in testing the correlation between a person's annual income and their overall happiness score based on a robust questionnaire that yields a standardized score. The researcher does not believe that a person's annual income will significantly impact their happiness, either positively or negatively. A large random sample of individuals is collected to test the psychologist's claim.

a. Determine what population parameter is being tested:

pp

b. Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test:

< : left-tailed

> : right-tailed

: two-tailed

4. The restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits:

48	45	44	43	46	47
42	46	47	45	47	49

Note: The data appears to be approximately normally distributed.

Test the bartender's ability to pour 45 mL at the 5% level of significance.

T-Distribution Table

a. Calculate the sample mean and standard deviation.

x=x=

Round to three decimal places if necessary

s=s=

Round to three decimal places if necessary

b. Calculate the test statistic.

t=t=

Round to three decimal places if necessary

c. Determine the critical value(s) for the hypothesis test.

• +

Round to three decimal places if necessary

d. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

5. H0:=10kgH0:=10kg H1:>10kgH1:>10kg Level of significance: =0.05=0.05 Sample size: n=36n=36 Test statistic: t=1.944t=1.944 Unknown population standard deviation

T-Distribution Table

a. Determine the critical value(s) for the proposed hypothesis test.

• +

Round to three decimal places if necessary

b. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

c. State the decision error type that is possible.

Type I Error

Type II Error

6. In a sample of 80 borrowers who borrowed less than $1,000 from an online instant lender, 20 repaid late while in a sample of 120 who borrowed over $1,000, 42 repaid late. Is there enough evidence to conclude that those who borrow less than $1,000 are less like likely to repay late? Test at =0.025.=0.025.

Standard Normal Distribution Table

a. Calculate the test statistic. Let p1p1 be the proportion for borrowers who borrowed less than $1,000 and p2p2 be those who borrowed over $1,000.

z=z=

Round to two decimal places if necessary

Enter 0 if normal approximation cannot be used

b. Determine the critical value(s) for the hypothesis test.

• +

Round to two decimal places if necessaryEnter 0 if normal approximation cannot be used

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

Cannot Use Normal Approximation

7. A phone company plans on offering their new smartphone in four colours: white, black, silver and rose gold. They anticipate that 30% of shoppers will prefer white, 35% will prefer black, 20% will prefer silver and 15% will prefer rose gold. They perform market research by asking a random sample of 350 potential customers which colour they prefer.

Colour	White	Black	Silver	Rose Gold
Frequency	100	129	88	33

Can the company conclude that their expected distribution was accurate using a 10% level of significance?

Chi Square Distribution Table

a. Calculate the test statistic.

2=2=

Round to two decimal places if necessary

b. Determine the critical value(s) for the hypothesis test.

• +

Round to two decimal places if necessary

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject