statistics

• 
  

  $9\pm1.4$

• $9\pm1.7$

• $9\pm2.07$
  

• $9\pm2.0$
  

A school psychologist at a large high school took a random sample of 16 students and asked them how much sleep they get on a typical weekend night. The sample data were roughly symmetric with a mean of 8.75

and a standard deviation of 1.5

Based on this sample, which of the following is a 90%

confidence interval for the mean amount of sleep (in hours) this population of students gets on a typical weekend night?

• $8.75\pm0.617$

• $8.75\pm0.657$

• $8.75\pm0.799$

• $8.75\pm1.5$

Caviar is an expensive delicacy, so companies that package it pay very close attention to the amount of product in their tins. Suppose a company that produces over 1000 tins of caviar per day took an SRS of 20

tins from one day's production. The sample showed a mean of 99.8g of caviar per tin with a standard deviation of 0.9g. The amounts were roughly symmetric with no outliers.

Based on this sample, which of the following is a 95%

confidence interval for the mean amount of caviar (in grams) per tin from that day's production?

• $99.8\pm1.96\left(\frac{0.9}{\sqrt{20}}\right)$

• $99.8\pm2.093\left(\frac{0.9}{\sqrt{20}}\right)$

• $99.8\pm1.96\left(0.9\right)$

• $99.8\pm2.093\left(0.9\right)$

A safety auditor at a paint factory took a random sample of 25 cans of paint from a production run of over

1,000 cans and measured the amount of lead in each can of paint in the sample. The sample data were roughly symmetric with a mean of 37 parts per million (ppm) of lead per can and a standard deviation of 18ppm.

Based on this sample, which of the following is a

95% confidence interval for the mean amount of lead per can of paint (in ppm) in this production run?

• (29.57,44.43)

• (29.94,44.06)

• (30.84,43.16)

• (31.08,42.92)

Fatimah wants to build a one-sample z interval to estimate the proportion of students at her school who ate breakfast every day last week with 90%

confidence. She takes a random sample of 75

students and finds that 20 ate breakfast every day last week.

What critical value z*

should Fatimah use to construct this confidence interval?

• z* = 1.282

• z* = 1.645

• z* = 1.96

• z* = 2.576

Jonah wants to make a one-sample z interval using 99%

confidence to estimate what proportion of silicon wafers at his factory are defective. He wants the margin of error to be no more than 3% . A previous study suggests that about 6% of these wafers are defective.

If we assume ^ p=0.06 , what is the smallest sample size required to obtain the desired margin of error?

• 234

• 416

• 598

• 936

A polling firm wants to use a one-sample z

interval to estimate what proportion of voters in a country plan on voting for a certain candidate. They want the margin of error to be no more than ±3% at 99%

confidence.

What is the smallest sample size required to obtain the desired margin of error?

• 1520

• 1844

• 2136

• 4148

Fatimah wants to estimate the proportion of students at her school who ate breakfast every day last week. She takes an SRS of 80 of the 1000students at her school and finds that 20 of those sampled ate breakfast every day last week.

Based on this sample, which of the following is a 95%, percent confidence interval for the proportion of all students at the school who ate breakfast every day last week?

• $20\pm0.080$

• $20\pm0.095$

• $0.25\pm0.080$

• $0.25\pm0.095$

Leandro wants to estimate the proportion of light bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that 25 arrived broken. He's willing to assume independence between bulbs in the sample.

Based on this sample, which of the following is a 90%, percent confidence interval for the proportion of bulbs that arrive broken?

• $0.05\pm1.645\sqrt{\frac{0.05\left(0.95\right)}{500}}$

• $0.05\pm1.96\sqrt{\frac{0.05\left(0.95\right)}{500}}$

• $25\pm1.645\sqrt{\frac{25\left(475\right)}{500}}$

• $0.05\pm1.96\sqrt{\frac{25\left(475\right)}{500}}$

A fast-food restaurant has an automated beverage machine that dispenses a set amount of liquid based on a size setting. Suppose that on the medium setting, the standard deviation of the amounts dispensed is

σ=17 mL . The manager of the restaurant plans on taking a sample of n medium drinks to construct a 99%

confidence interval for the mean amount of liquid dispensed. They want the margin of error to be no more than 10 mL.

Which of these is the smallest approximate sample size required to obtain the desired margin of error?

• 12 drinks

• 20 drinks

• 30 drinks

• 40 drinks