Unit 6: Mixed Confidence Intervals Practice

Choose the appropriate confidence interval for the situation:

A random sample of 30 movie theaters showed that the average price for a movie was $10 with a standard deviation of $1.20.

• z confidence interval for a mean

• t confidence interval for a mean

• z confidence interval for a proportion

• t confidence interval for a proportion

Tags

CCSS.HSS.ID.A.4

Choose the appropriate confidence interval for the situation:

After watching a horror film, 34 out of 50 people reported problems getting to sleep.

• z confidence interval for a mean

• t confidence interval for a mean

• z confidence interval for a proportion

• t confidence interval for a proportion

A factory that produces manhole covers took a random sample of 800 manhole covers and found that 40 out of the covers were defective. What is the 95% CI for the proportion of defective manhole covers?

• (37.26, 42.74)

• (.035, .065)

• (.047, .053)

• (.015, .085)

Tags

CCSS.HSS.IC.B.4

The scores of a certain population on the Wechscler Intelligence Scale for Children (WISC) are thought to be normally distributed with mean $\mu$  and standard deviation $\sigma=10$  .  A simple random sample of 10 children from this population is taken, and each is given the WISC.  The 95% confidence interval for $\mu$  ,  $\overline{x}\pm1.96\frac{10}{\sqrt{10}}$ , is computed from these scores.  A histogram of the 10 WISC scores is shown.

Based on this histogram, we would conclude that:

• the 95% confidence interval computed from these data is very reliable.

• the 95% confidence interval computed from these data is not very reliable.

• the 95% confidence interval computed from these data is actually a 99% confidence interval.

• the 95% confidence interval computed from these data is actually a 90% confidence interval

• only one student's score should fall outside the 95% confidence interval.

An agricultural researcher plants 25 plots with a new variety of corn. The average yield for those plots is $\overline{x}=150$ bushels per acre.  Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean $\mu$  and standard deviation $\sigma=10$  bushels.  A 90% confidence interval for $\mu$  is:

•  $150\pm2.00$  

•  $150\pm3.29$  

•  $150\pm3.92$  

•  $150\pm16.45$  

•  $150\pm32.90$  

An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average yield for those plots is found to be $162.72\pm4.47$ bushels per acre.  Which of the following would produce a confidence interval with a smaller margin of error than this 90% confidence interval?

• Choosing a sample with a larger standard deviation

• Planting 100 plots, rather than 25

• Choosing a sample with a smaller standard deviation

• Planting only 5 plots rather than 25

• None of the above

An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is $\overline{x}=150$ bushels per acre.  Assume that the yield per acre for the new variety of corn is normally distributed with unknown mean $\mu$ and that a 90% confidence interval for $\mu$ is found to be $150\pm3.29.$  What can we deduce about the standard deviation $\sigma$ of the yield per acre for the new variety of corn?  

•  $\sigma$  is about 10

•  $\sigma$ will be larger than 10 if we use 100 plots 

•  $\sigma$ is 3.29 

• If we repeated the experiment many, many additional times and from each computed a 90% confidence interval, $\sigma$ would be within 3.29 of the mean in approximately 90% of the intervals 

•  $\sigma$ will vary depending on the sample size 

A random sample of 200 New York State voters included

88 Republicans, while a random sample of

300 California voters produced 141 Republicans.

Which of the following represents the 95% confidence

interval that should be used to estimate the

true difference in the proportions of Republicans

in New York State and California?

• 
• 
• 
• 
• 

To assess the accuracy of a laboratory scale, a standard weight that is known to weight 1 gram is repeatedly weighed a total of n times, and the mean $\overline{x}$ of the n weighings is computed.  Suppose the scale readings are normally distributed with unknown $\mu$ and standard deviation $\sigma=0.01\ grams.$  How large should n be so that a 95% confidence interval for $\mu$ has a margin of error of $\pm\ 0.0001?$   

• 100

• 196

• 385

• 10,000

• 38,416

James, the owner of a fitness club franchise, was interested in comparing the level of physical fitness of the members of his gym and the members of a competitor’s gym down the street. He selected a random sample of 125 members of his gym and found 75 of them could pass a standard fitness test. He also selected a random sample of 95 members of the competitor’s gym and found that 70 of them could pass the physical fitness test. Which of following estimates with 96% confidence, the difference in proportion of members of James’ gym who can pass the standard fitness test and the proportion of members of his competitor’s gym who can pass the standard fitness test?

• A. ( 0.2404, 0.0333)

• B. ( 0.2602, 0.0135)

• C. ( 0.2661, 0.0076)

• D. ( 0.3490, 0.1099)

• E. ( 0.3547, 0.1042)