# Probability, confidence interval, analysis sample questions

The area under the normal curve between z=1 and z=2 is ________________ the area under the normal curve between z=2 and z=3.

A. Greater than

B. Less than

C. Equal to

D. A, B or C above dependent on the value of the mean

E. A, B or C above dependent on the value of the standard deviation

Essay Type Questions Please show work and formula's Answers in Microsoft Word format (Copy Excel to Word)

In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 12 teachers who have recently left their profession. Find the probability that at least 7 of them were laid off.

The weight of a product is normally distributed with a standard deviation of 1.5 ounces. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 15 ounces?

A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.4 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 49 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes being greater than 4.35.

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.32 inches. A sample of 16 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.95 and 30.25 inches long?

The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments for the orders. The planner randomly selected 900 orders and found that 180 orders were shipped late. Construct the 95% confidence interval for the proportion of orders shipped late.

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#### Solution Preview

The area under the normal curve between z=1 and z=2 is ________________ the area under the normal curve between z=2 and z=3. A. Greater than B. Less than C. Equal to D. A, B or C above dependent on the value of the mean E. A, B or C above dependent on the value of the standard deviation Choose A: greater than. Reason: the area under the normal curve is increasing for positive value of z.

Essay Type Questions Please show work and formula's Answers in Microsoft Word format (Copy Excel to Word)

In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 12 teachers who have recently left their profession. Find the probability that at least 7 of them were laid off.

Let X be the number of teachers who have recently left their profession, then X~Binomial(12, 0.30). Using ...

#### Solution Summary

The soluton gives detailed steps on answering 6 quesitons by applying property of normal distribution to calculate both probability and confidence interval.

Statistics Questions

1. Increasing the number of scores in a sample from n = 10 to n = 20 will increase the width of a confidence interval to estimate the population mean. (Assume all other factors are held constant.)

True

False

2. An educational psychologist gives a group of third-grade students a reading test at the beginning of the school year and again at the end of the year. The psychologist wants to use the data to estimate how much reading scores change during the year. The psychologist should use the independent-measures t statistic for the estimation.

True

False

3. A researcher uses a sample of n = 25 scores to construct a 90% confidence interval to estimate an unknown population mean. The correct interpretation of the confidence interval is:

None of these.

If another sample of n = 25 scores was selected, there is a 90% probability that the sample mean will be in the interval.

All of these.

There is a 90% probability that the unknown population mean is in the interval.

4. If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 1.00.

True

False

5. In an analysis of variance, if all other factors are held constant, the larger the differences between the sample means, the bigger the value for the F-ratio.

True

False

6. The F-ratio for an analysis of variance comparing two treatments with n = 10 in each treatment would have df = 2, 18.

True

False

7. In an analysis of variance, which of the following is directly influenced by the size of the sample mean differences?

SS total

SS within treatments

All three SS values are influenced.

SS between treatments

8. Which of the following is not normally calculated as part of an analysis of variance?

MS total

SS total

SS within

MS within

9. A researcher uses an analysis of variance to test for mean differences among three treatment conditions using a sample of n = 10 participants in each treatment. The F-ratio from this analysis would have

df = 2, 29

df = 2, 27

df = 3, 27

df = 29

10. A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study. Based on the df values, how many treatments were compared in the study and what was the total number of participants participating in the study?

2 treatments and 35 participants

3 treatments and 37 participants

4 treatments and 40 participants

4 treatments and 36 participants