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Review of Chapter 7

Confidence Intervals

1. A NAPA Auto Parts supplier wants information about how long car owners plan to

keep their cars. A random sample of 21 car owners results in a mean of 7 years,

with a standard deviation of 3.75 years. Find a 95% confidence interval for the

true population mean.

2. In a gallop poll of 200 adults, 93% said that restaurants and bars should refuse

service to patrons who had too much to drink. Find a 95% confidence interval for

the true percentage of patrons with this view.

3. Among those taking the Graduate Record Exam, 80 people are randomly selected.

This group had a mean score of 550 and a population standard deviation of 140.

What is the 95% confidence interval for the population mean for the GRE test.

For two populations:

Look at the difference between the two groups (means or proportions).

Is the difference 0?

Confidence Interval Interpretations

(–, +) means 0 is in the interval, there is no difference in the groups

(–, –) means group 1 is smaller than group 2, since the subtraction is negative

(+ , +) means group 1 is bigger than group 2, since the subtraction is positive

Calculator Commands

One group Two groups

7: z interval 9: 2 sampzint

8: tinterval 0: 2 samptint

A: 1propzint B 2 propzint

Confidence Levels from significance levels (Given α not a confidence level)

For a “two tailed” question use the opposite of alpha

Example: 0.5 significance means 0.95 confidence

01. significance means 0.99 confidence

For a “one tailed” question use the opposite of 2 times alpha

Example: 0.5 significance means 0.90 confidence

0.10 significance means 0.80 confidence

Use a Confidence Interval to Solve Each Problem 1-3

1. Graduates of a two-year associate degree nursing program (AND) and graduates of a four-year baccalaureate nursing program (BSN) both take the same certificate exam for licensure as a registered nurse. It has been argued that the two-year program is too short, and that undergraduate nursing education should be standardized to a four-year program. The state board exam scores for AND and BSN graduates are considered. Of 80 AND graduates, 60 passed. Of 115 BSN graduates, 95 passed. Use a 95% confidence interval to determine if the two groups perform differently?

2. A neonatal nurse practitioner at a local neonatal intensive care unit is interested in the effect of light on infant’s amount of sleep. She randomly selects infants from the unit and places them in two categories. Category A consists of a normal ICU surroundings and lighting. Category B is comprised of a specially designed light controlled dim room apart from the general population. The nurses involved in the study write down how many hours the infants are asleep throughout the day. Use a 90% confidence interval to determine whether the sleep lengths are shorter for the group in normal lighting than those in the dim rooms?

Category A (normal) n = 31 [pic] = 18.67 s = 1.97

Category B (dim) n = 41 [pic] = 20.63 s = 1.58

3. A school experiments with two teaching approaches for mathematics. In one classroom the material is taught using lectures only. In the other classroom lectures are mixed in with the use of manipulatives, computers, and collaborative activities. Use a 90% confidence interval to decide whether the data below support the claim that students in the classroom with multiple techniques do better.

Lecture n = 20 [pic] = 76.0 s = 2.1

Multiple n = 32 [pic] = 88.5 s = 0.4

“Homework #3” 10 points

Use Confidence Intervals to Answer Each Problem

1. To test the effectiveness of a new cholesterol drug, “Lo-chol”, 600 women were split into 2 groups of equal size. The control group used no drug to lower cholesterol but followed a diet and exercise routine. The experimental group followed the same routine, but also took the Lo-chol pill each day. The Lo-chol group had a mean reduction of 30 points with a σ of 5. The control group had a mean reduction of 23 points with a σ of 4. Use a 95% confidence interval to decide if there is there evidence that Lo-chol is an effective cholesterol-reducing drug?

2. Two groups were asked to rate a soft drink. One group knew the brand name of the cola they were drinking before they rated it. The other group did not know the brand name. Does a 90% confidence interval indicate that is there a difference in the groups’ ratings of the cola when knowing which kind it is?

Know 8 2 6 10 9 2 8 10 1 6

Don’t Know 6 3 7 7 6 1 6 8 2 4

3. A group of 250 men took the NJCBSPT and 150 passed the algebra portion. A group of 350 women took the test and 290 passed. Does a 99% confidence interval for this data support that men’s success rates are lower than women’s?

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