Chapter 7 Practice

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A national poll found that 881 out of 1013 randomly selected adults said they always wear seat belts. Construct and interpret a 98% confidence interval for the proportion of adults who always wear seat belts. Interpret the interval results. 

• (0.8451, 0.8943)

• (0.8623, 0.9125)
• (0.8012, 0.8514)
• (0.8431, 0.8929)

A professor wants to conduct a survey regarding student prerequisite knowledge for College Algebra.  She studies the placement test scores and is told that the population standard deviation is 6.72.  How many students would she need for her study if she wants to build a 95% confidence interval with a margin of error of 2 points? 

• 44

• 50

• 78

• 23

A random sample of 40 visitors to a certain theme park determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day. Assuming that the population standard deviation of the amount spent per person is $15, construct and interpret a 95% confidence interval for the mean amount spent daily per person at the theme park.

• 87.50 to 95.62
• 88.78 to 98.08

• 85.62 to 93.75
• 89.47 to 97.39

A simple random sample of size 42 has a mean of 3.43 and a standard deviation of 1.51. Construct a 98% confidence interval for the population mean.

There is no information given about ​ (a)   .

Since ​ (b)   is unknown, we cannot use the ​ (c)   method.

Next, we must determine whether ​ (d)   .The sample size is 42.

We should then use the ​ (e)   method.

• σ
• Z
• n>30
• t
• s
• np>10

A simple random sample of size 11 has a mean of 3.16. The population standard deviation is 1.75. The population is approximately normally distributed. Construct a 98% confidence interval for the population mean.

We are asked to find a confidence interval for the ​ (a)   .

σ is ​ (b)   .

The sample size is ​ (c)   , so it is not greater than 30.

The population is approximately normal. Hence, we should use the ​ (d)   method.

• known
• population mean
• z
• 11
• unknown
• 98%
• t
• sample mean

How many students would they need in their sample in order to have a 4% margin of error for a 95% confidence interval? 

• 150
• 601
• 300
• 450

Another school in the region conducted a similar study and had a support percentage of 35%. Use this information to estimate the sample size needed in order to have a 4% margin of error for a 95% confidence interval. 

• 100
• 200
• 547

• 355

The student organization sponsor got impatient and decided to draw a SRS of 300 students and just use whatever margin of error is calculated. The survey indicated that 120 of those students support the plan for new bike trails around campus. Find a 95% confidence interval to estimate the population proportion of all students at this school who support the bike trails. Include your calculations for margin of error and interpret the results.

• (0.200, 0.300)
• (0.400, 0.500)
• (0.345, 0.455)

• (0.348, 0.452)

A simple random sample of 35 colleges and universities in New York State had a mean tuition of $30,577 with a standard deviation of $6,232.  Construct a 99.7% confidence interval for the mean tuition for all colleges and universities in New York State. Interpret the interval results.

• 27210,33944

• 25484,48621

• 24856,22554

• 27541,36952