6.2: Errors and Power Assignment

Your local Starbucks is hoping to cut back on the wait time for their customers. The proportion of drive-through customers who wait longer than 3 minutes to get their coffee is p = 0.76. In an effort to reduce this, the manager assigns an extra employee to help make the orders in the morning. During the next month, the manager will select an SRS of customer wait times and determine if the proportion who are waiting longer than 3 minutes has decreased.

a) What is the parameter of interest in this problem?​ (a)  

• p=true prop of who wait more than 3 min.
• p=true prop of who wait than 3 min.
• p=true prop of who wait less than 3 min.

Your local Starbucks is hoping to cut back on the wait time for their customers. The proportion of drive-through customers who wait longer than 3 minutes to get their coffee is p = 0.76. In an effort to reduce this, the manager assigns an extra employee to help make the orders in the morning. During the next month, the manager will select an SRS of customer wait times and determine if the proportion who are waiting longer than 3 minutes has decreased.

b) State the null hypothesis ​ ​ (a)   and alternative hypothesis​ (b)   .

• p=.76
• p<.76
• p>.76
• p does not equal .76

Your local Starbucks is hoping to cut back on the wait time for their customers. The proportion of drive-through customers who wait longer than 3 minutes to get their coffee is p = 0.76. In an effort to reduce this, the manager assigns an extra employee to help make the orders in the morning. During the next month, the manager will select an SRS of customer wait times and determine if the proportion who are waiting longer than 3 minutes has decreased.

c) Type I error:​ Saying we ​ (a)   reduce the wait times when we really ​ (b)   .

Consequences: ​ The manager ​ (c)   tray anything else to reduce the wait time.

• did
• didn't
• will not
• will

Your local Starbucks is hoping to cut back on the wait time for their customers. The proportion of drive-through customers who wait longer than 3 minutes to get their coffee is p = 0.76. In an effort to reduce this, the manager assigns an extra employee to help make the orders in the morning. During the next month, the manager will select an SRS of customer wait times and determine if the proportion who are waiting longer than 3 minutes has decreased.

d) Type II Error: Saying the wait times ​ ​ (a)   decrease when they really ​ (b)   .

Consequences: The manager ​ (c)   keep trying to decrease the wait times ​ (d)   .

• did not
• will
• unnecessarily
• will not
• necessarily

Failing to reject a null hypothesis that is false can be characterized as

• a Type I error

• a Type II error

• both a Type I and Type II error

• the power of a test

• no error

Which of the following accurately describes the power of a statistical test of hypothesis?

• It is equal to the p-value

• It is equal to 1-(p-value)

• It is equal to 𝛼, the significance level.

• It is the probability that a test using a fixed value of 𝛼 will reject 𝐻0 when a particular alternative value of the parameter is true.

• It is equal to 𝛽

For a given hypothesis test, the probability of a Type I error is represented by 𝛼 and the probability of a Type II error is represented by 𝛽. Which of the following represents the power of the test?

• 𝛼

• 1 − 𝛼

• 𝛽

• 1-𝛽

• 𝛼 + 𝛽

Which of the following statements is/are correct?

I. The power of a significance test depends on the value of the test statistic.

II. The probability of a Type II error is equal to the significance level of the test.

III. You can only find errors if you have a significance level determined.

• I and II only

• I and III only

• II and III only

• I, II, and III

• None of the above gives the complete set of correct responses.

Which of the following increases the power of a significance test?

• Using a two-tailed test instead of a one-tailed test.

• Decreasing the size of your sample.

• Finding a way to increase the population standard deviation.

• Increasing the significance level.

• Perform the test many times using the same data.