Find the Mistake
Interpretation
Hard Problems
(Not on Quiz)
100

1. State the Hypothesis

H0: u=10

H1: u<10

1. State the Hypothesis

H0: u=10 (The average customer spends $10 and the bar should close)

H1: u>10 (The average customer spends more than $10 and the bar should remain open)

100

Interpret the following in the context of the problem.

The null hypothesis is true.

The average customer spends $10.

100

What is the lowest possible p value?

0

200

2. Gather the data

x̄ = $11.24

s = $5.69

n = 30

Here, x̄ is the average amount of money spent by all customers

2. Gather the data

x̄ = $11.24

s = $5.69

n = 30

Here, x̄ is the average amount of money spent by the customers in our sample

200

Interpret the following in the context of the problem.

We reject the null hypothesis.

We believe the average customer spends more than $10.

200

What is the highest possible p value?

1

300

3. We first assume that the null hypothesis is true

We assume that the average customer spends less than $10.

3. We first assume that the null hypothesis is true

We assume that the average customer spends $10

300

What would a type I error be in this scenarior?

We believe the average customer spends more than $10 when they in reality do not.

300

What would the result of a hypothesis test be if the significance level was 1?

The test would always reject the null hypothesis
400

4. Use the Central Limit Theorem

x̄ ~ N(11.24,0.19)

3. Use the Central Limit Theorem

x̄ ~ N(u,s/sqrt(n))

x̄ ~ N(10,5.69/sqrt(30))

x̄ ~ N(10,1.04)

400
If the significance level was 5%, what would the probability of not getting a Type I error?

95%

400

What would the result of a hypothesis test be if the significance level was 0?

The hypothesis test would always fail to reject.

500

5. Draw a picture of the distribution of the sample averages

see photos

5. Draw a picture of the distribution of the sample averages

Because we are using a alternative hypothesis H1:u>10 we should shade in the area to the right of the sample average

500

What would power be in this scenario?

Power is the ability to correctly reject a false null hypothesis.

Power is the ability to correctly conclude that the bar should remain open when the average customer does spend more than $10.

500

When would the p value of a hypothesis test with a not equal to alternative hypothesis be 1?

When the null hypothesis is the sample average

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