Inference Calculator Review

Inference Calculator Review

By Joni Hutcherson

Your calculator can do the math on all the tests and intervals we have learned this semester

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Go to Stat->Tests​

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​Look at your ​handout to see which test does what

Inference on the Calculator​

Let's Practice

We will do a few examples together, and then you will work with a team to practice some more!

Example 1

A school counselor wants to know how smart the students in her school are. She gets funding from the principal to give an IQ test to a random sample of 60 of the over 1000 students in the school. The mean IQ score was 114.98 and the standard deviation was 14.80

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Construct a 90% confidence interval for the mean IQ score of students at the school.

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Things to think about: What type of interval?

Which calculator command?

Do we have data or stats?​

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Fill in the Blank

Type in the interval your calculator gave you.

Round to two decimal places and do not use any spaces.

Be sure you put parentheses and a comma.

Example answer

(1.23,5.67)

Example 2

35 people from a random sample of 125 workers from Company A admitted to using sick leave when they weren't really ill. 17 employees from a random sample of 68 workers from Company B admitted the same thing. Does this data provide evidence that there is a difference in the proportion of employees who use sick leave when they are not ill at the two companies?

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Things to think about: What type of test?

Which calculator command?

Do we have data or stats?​

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Fill in the Blank

What was the value of the statistic the calculator gave you?

(z, t, or $$\chi^2$$  )

Round to three decimal places.

Fill in the Blank

What is the p-value the calculator gave you?

Round to three decimal places.

Open Ended

Does this data provide evidence that there is a difference in the proportion of employees who use sick leave when they are not ill at the two companies?

What would your conclusion statement for this problem be?

Example 3

Does the use of fancy type fonts slow down the reading of text on a computer? Adults can read four paragraphs of text in the common Times New Roman font in an average of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate font named Gigi. Here are their times in seconds. Do the data suggest that the fancy font type slowed down reading times?

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Things to think about: What type of test?

Which calculator command?

Do we have data or stats?​

​23.2	21.2​	28.9	27.7​	29.1​	27.3​	16.1​	22.6​	25.6​	34.2​	23.9​	26.8​
​20.5	34.3​	21.4​	32.6	26.2​	34.1​	31.5​	24.6​	23.0​	28.6​	24.4​	28.1​

Fill in the Blank

What was the value of the statistic the calculator gave you?

(z, t, or $$\chi^2$$  )

Round to three decimal places

Fill in the Blank

What is the p-value the calculator gave you?

Round to five decimal places.

Open Ended

Do the data suggest that the fancy font type slowed down reading times?

What would your conclusion statement for this problem be?

Now it's your turn to practice

• Get into groups of 3-4 people​

• Only one person on your team can have a calculator.

  • Everyone else put your calculator away.​

  • You will trade off who has the calculator for each new scenario.​

• Only one person on your team can have a computer.​

  • Everyone else, log out and close your computer.​

• We will work through 9 scenarios, each with several questions for you to answer.

• This counts as your 9-weeks test grade!​

  • First Place gets a 100

  • Second Place gets a 95

  • Third Place gets a 90

  • And so on...No one will get a grade lower than their actual group score total.​

Scenario One

​The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. The manager selected a random sample of 80 customers who asked for a water cup when placing an order and found that 23 of those customers filled the cup with a soft drink from the beverage fountain.

Multiple Choice

What type of inference procedure would you do?

• One sample z interval

• One sample t interval

• Two sample z interval

• Two sample t interval

• Paired t interval

Fill in the Blank

The manager selected a random sample of 80 customers who asked for a water cup when placing an order and found that 23 of those customers filled the cup with a soft drink from the beverage fountain.

Calculate a 95% confidence interval.

No spaces, round to three decimal places.

Scenario Two

A pharmaceutical company has developed a new drug to reduce cholesterol. A regulatory agency will recommend the new drug for use if there is convincing evidence that the mean reduction in cholesterol level after one month of use is more than 20 milligrams/deciliter (mg/dl), because a mean reduction of this magnitude would be greater than the mean reduction for the current most widely used drug.​

​The pharmaceutical company collected data by giving the new drug to a random sample of 50 people from the population of people with high cholesterol. The reduction in cholesterol level after one month of use was recorded for each individual in the sample, resulting in a sample mean reduction and standard deviation of 24 mg/dl and 15 mg/dl, respectively.

Multiple Choice

What type of inference procedure would you do?

• One sample z interval

• One sample t interval

• Two sample z interval

• Two sample t interval

• Paired t interval

Fill in the Blank

The pharmaceutical company collected data by giving the new drug to a random sample of 50 people from the population of people with high cholesterol. The reduction in cholesterol level after one month of use was recorded for each individual in the sample, resulting in a sample mean reduction and standard deviation of 24 mg/dl and 15 mg/dl, respectively.

Calculate a 99% confidence interval.

No spaces, round to three decimal places.

Scenario Three

​A researcher conducted a medical study to investigate whether taking a low-dose aspirin reduces the chance of developing colon cancer. As part of the study, 1,000 adult volunteers were randomly assigned to one of two groups. Half of the volunteers were assigned to the experimental group that took a low-dose aspirin each day, and the other half were assigned to the control group that took a placebo each day. At the end of six years, 15 of the people who took the low-dose aspirin had developed colon cancer and 26 of the people who took the placebo had developed colon cancer.

At the significance level α = 0.05, do the data provide convincing statistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers?

Multiple Choice

What type of test should you use?

• One sample t test

• One sample z test

• Two sample t test

• Two sample z test

• Chi Square Test

Multiple Choice

What is the appropriate alternative hypothesis for this test?

• $$H_a:\ p_{aspirin}-p_{placebo}<0$$  

• $$H_a:\ p_{aspirin}-p_{placebo}>0$$  

• $$H_a:\ p_{aspirin}-p_{placebo}\ne0$$  

• $$H_a:\ p_{aspirin}-p_{placebo}=0$$  

Fill in the Blank

As part of the study, 1,000 adult volunteers were randomly assigned to one of two groups. At the end of six years, 15 of the people who took the low-dose aspirin had developed colon cancer and 26 of the people who took the placebo had developed colon cancer.

What is the test statistic the calculator gave you?

Round to three decimal places.

Fill in the Blank

What was the p-value the calculator gave you?

Round to three decimal places.

Open Ended

At the significance level α = 0.05, do the data provide convincing statistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers?

What would your conclusion statement for this scenario be?

A parent advisory board for a certain university was concerned about the effect of part-time jobs on the academic achievement of students attending the university. To obtain some information, the advisory board surveyed a simple random sample of 200 of the more than 20,000 students attending the university. Each student reported the average number of hours spent working part-time each week and his or her perception of the effect of part-time work on academic achievement. The data in the table below summarize the students’ responses by average number of hours worked per week (less than 11,

11 to 20, more than 20) and perception of the effect of part-time work on academic achievement (positive, no effect, negative).

Scenario Four

Multiple Choice

What type of test should you use?

• One sample t test

• One sample z test

• Two sample t test

• Two sample z test

• Chi Square Test

Multiple Choice

What is the appropriate null hypothesis for this test?

• There is an association between hours worked and the perception of effect on academic achievement.

•  There is no association between hours worked and the perception of effect on academic achievement.

• There is a difference between the distribution of hours worked and the perception of effect on academic achievement. 

•  There is no difference between the distribution of hours worked and the perception of effect on academic achievement. 

Fill in the Blank

What is the test statistic the calculator gave you?

Round to three decimal places.

Fill in the Blank

What was the p-value the calculator gave you?

Round to three decimal places.

Open Ended

Do the data provide evidence of an association?

What would your conclusion statement for this scenario be?

A large company has two shifts—a day shift and a night shift. Parts produced by the two shifts must meet the same specifications. The manager of the company believes that there is a difference in the proportions of parts produced within specifications by the two shifts. To investigate this belief, random samples of parts that were produced on each of these shifts were selected. For the day shift, 188 of its 200 selected parts met specifications. For the night shift, 180 of its 200 selected parts met specifications.

Scenario Five

Multiple Choice

What type of inference procedure would you do?

• One sample z interval

• One sample t interval

• Two sample z interval

• Two sample t interval

• Paired t interval

Fill in the Blank

For the day shift, 188 of its 200 selected parts met specifications.

For the night shift, 180 of its 200 selected parts met specifications.

Calculate a 95% confidence interval for the difference in the number of parts that meet specifications for the two shifts. Round to three decimal places, no spaces.

A researcher conducted a study to investigate whether local car dealers tend to charge women more than men for the same car model. Using information from the county tax collector’s records, the researcher randomly selected one man and one woman from among everyone who had purchased the same model of an identically equipped car from the same dealer. The process was repeated for a total of 8 randomly selected car models.  The purchase prices and the differences (woman – man) are shown in the table below.

Scenario Six

Multiple Choice

What type of test should you use?

• Two sample t test

• Two sample z test

• Paired t test

• Paired z test

• Chi Square Test

Multiple Choice

What is the appropriate alternative hypothesis?

• $$H_a:\ \mu_{dif}>0$$  

• $$H_a:\ \mu_{dif}=0$$  

• $$H_a:\ \mu_{dif}<0$$  

• $$H_a:\ \mu_{dif}\ne0$$  

Fill in the Blank

What is the test statistic the calculator gave you?

Round to three decimal places.

Fill in the Blank

What was the p-value the calculator gave you?

Round to three decimal places.

Multiple Choice

What is the correct conclusion for this scenario at a significance level of $$\alpha=0.01$$  ?

• Since p is less than $$\alpha$$  we reject the null hypothesis.

  There is evidence that women are charged more than men for cars.

• Since p is less than $$\alpha$$  we fail to reject the null hypothesis.

  There is evidence that women are charged more than men for cars.

• Since p is less than $$\alpha$$  we reject the null hypothesis.

  There is not evidence that women are charged more than men for cars.

• Since p is less than $$\alpha$$  we fail to reject the null hypothesis.

  There is not evidence that women are charged more than men for cars.

Patients with heart-attack symptoms arrive at an emergency room either by ambulance or self-transportation provided by themselves, family, or friends. When a patient arrives at the emergency room, the time of arrival is recorded. The time when the patient’s diagnostic treatment begins is also recorded.

An administrator of a large hospital wanted to determine whether the mean wait time (time between arrival and diagnostic treatment) for patients with heart-attack symptoms differs according to the mode of transportation. A random sample of 150 patients with heart-attack symptoms who had reported to the emergency room was selected. For each patient, the mode of transportation and wait time were recorded. Summary statistics for each mode of transportation are shown in the table below.​

Scenario Seven

Multiple Choice

What type of inference procedure would you do?

• One sample z interval

• One sample t interval

• Two sample z interval

• Two sample t interval

• Paired t interval

Fill in the Blank

Calculate a 95% confidence interval for the difference in wait time for people who arrive in ambulances and who transport themselves.

Round to three decimal places, no spaces.

Multiple Choice

Does this interval provide evidence of a difference in wait times for people who arrive in ambulances and people who transport themselves?

• Yes

• No

Some boxes of a certain brand of breakfast cereal include a voucher for a free video rental inside the box. The company that makes the cereal claims that a voucher can be found in 20 percent of the boxes. However, based on their experiences eating this cereal at home, a group of students believes that the proportion of boxes with vouchers is less than 0.2. This group of students purchased 65 boxes of the cereal to investigate the company’s claim. The students found a total of 11 vouchers for free video rentals in the 65 boxes. Based on this sample, is there support for the students’ belief that the proportion of boxes with vouchers is less than 0.2?​

Scenario Eight

Multiple Choice

What type of test should you use?

• Paired t test

• One sample z test

• Two sample t test

• Two sample z test

• Chi Square Test

Multiple Choice

What is the appropriate null hypothesis?

•   $$H_0:\ p=0.2$$  

• $$H_0:\ p\ne0.2$$   

•   $$H_0:\ p>0.2$$  

•   $$H_0:\ p<0.2$$  

Fill in the Blank

The students found a total of 11 vouchers for free video rentals in the 65 boxes.

What is the test statistic the calculator gave you?

Round to three decimal places.

Fill in the Blank

What was the p-value the calculator gave you?

Round to three decimal places.

Multiple Choice

What is the correct conclusion for this scenario at a significance level of $$\alpha=0.05$$  ?

• Since p is greater than $$\alpha$$  we reject the null hypothesis.

  There is evidence that the proportion of boxes with vouchers is less than 0.2

• Since p is greater than $$\alpha$$  we fail to reject the null hypothesis.

  There is evidence that the proportion of boxes with vouchers is less than 0.2

• Since p is greater than $$\alpha$$  we reject the null hypothesis.

  There is not evidence that the proportion of boxes with vouchers is less than 0.2

• Since p is greater than $$\alpha$$  we fail to reject the null hypothesis.

  There is not evidence that the proportion of boxes with vouchers is less than 0.2

The president of a large bank with many branch offices wanted to know if the quality of customer service at a new branch office was acceptable. One aspect of service that was examined was the length of time that customers had to wait in line before being helped by a member of the bank’s staff. The bank decided on acceptable probabilities for the waiting-time categories. To investigate whether the quality of customer service was acceptable, waiting times were recorded for a random sample of 100 customers at the new branch office. ​

The table below shows the acceptable probabilities they decided on and the numbers of customers observed in the five waiting-time categories.​

Scenario Nine

Multiple Choice

What type of test should you use?

• Chi Square

  Test for Goodness of Fit

• One sample z test

• One sample t test

• Two sample z test

• Chi Square

  Test for Independence

Multiple Choice

What is the appropriate alternative hypothesis?

• There is no difference between the acceptable probability distribution and the observed distribution.  

•   There is a difference between the acceptable probability distribution and the observed distribution.  

• There is no difference between the distribution of wait time categories.    

•   There is a difference between the distribution of wait time categories. 

Fill in the Blank

What is the test statistic the calculator gave you?

Round to two decimal places.

Fill in the Blank

What was the p-value the calculator gave you?

Round to three decimal places.

Multiple Choice

What is the correct conclusion for this scenario at a significance level of $$\alpha=0.10$$  ?

• Since p is greater than $$\alpha$$  we reject the null hypothesis.

  There is evidence that there is a difference in the acceptable and observed wait times.

• Since p is greater than $$\alpha$$  we fail to reject the null hypothesis.

  There is evidence that there is a difference in the acceptable and observed wait times.

• Since p is greater than $$\alpha$$  we reject the null hypothesis.

  There is not evidence that there is a difference in the acceptable and observed wait times.

• Since p is greater than $$\alpha$$  we fail to reject the null hypothesis.

  There is not evidence that there is a difference in the acceptable and observed wait times.