Confidence Interval
A 95% confidence interval for the true proportion of all families living in Smogsville who own an iPhone is (0.174, 0.246). Can we conclude that less than 30% of families in Smogsville own an iPhone?
Yes.
A research center claims that more than 55% of US adults regularly watch their local TV news. If you were to test this claim, what would your null and alternative hypotheses be?
H0: p = 0.55; H1: p > 0.55
In the standard normal distribution, find P(z < 0.87).
0.8078
Bert constructed a confidence interval to estimate the mean weight of students in his class. He used a sample of 30 students. Ruth constructed a confidence interval to estimate the mean weight of all adult males in her city. She based her CI on a sample of 5 adult males. Which CI is likely to give a better estimate of the mean it is estimating?
Bert's CI is likely a better estimate because his sample size is bigger.
Determine which of the following statements is a correct interpretation of a confidence interval.
A) A 95% confidence interval means that if a statistician repeats the survey over and over for many times, then about 95% of the confidence intervals constructed will contain the actual population mean.
B) For a 90% confidence interval, we can expect 90% of sample means to fall within the interval values.
C) A 95% confidence interval for the true mean weight (in pounds) of rat terrier dogs is (10, 18). This means that there is a 95% chance that a rat terrier dog will have a weight from 10 to 18 pounds.
A
In an advertisement, a grocery-delivery service claims that its mean delivery time is less than 29 minutes. A random sample of 39 deliveries has a sample mean of 27.9 minutes and a standard deviation of 3.4 minutes. What is the Test Statistic associated with a hypothesis test on the advertisment’s claim?
t = – 2.020
In a standard normal distribution, find the 30th percentile.
-0.524
To test the claim that the mean human body temperature is equal to 98.6°F, the following information was determined:
H0: µ = 98.6, H1: µ ≠ 98.6
α = 0.01, p-value = 0.0002, Reject H0
I have always been told the mean body temperature is 98.6°F. Have I been lied to my whole life?
Yes.There is sufficient evidence to warrant rejection of the claim that the mean human body temperature is equal to 98.6°F.
A physician wants to develop criteria for determining whether a patient’s pulse rate is atypical. A sample of 35 male patients produced a mean of 69.2 and a standard deviation of 12.8. Construct a 99% confidence interval estimate of the mean pulse rate for males.
We are 99% confident that the true mean pulse rate for males is between 63.2 and 75.1.
You are doing a study on food consumption of American teenagers. In a random sample of 250, you find that 41.6% of BPS students eat breakfast every day. Nationally, a research center estimates that number to be less than 40%. What is the P-value associated with a hypothesis test on the national claim?
0.6972
Based on data from the National Health and Nutrition Examination Survey, assume that weights of men are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds. If one man is randomly selected, find the probability that he weighs less than 174 pounds.
0.5275
To test a juice company’s claim that their bottles have a mean amount of juice of 15 oz, the following information was determined:
H0: µ = 15, H1: µ ≠ 15
α = 0.05, p-value = 0.2247, Fail to Reject H0
Does the company need to re-calibrate their machine?
No. There is not sufficient evidence to warrant rejection of the claim that the mean amount of juice is 15 oz.
A government statistician randomly selects 112 fast food workers from Maryland and finds that the average hourly wage is $11.25 with a standard deviation of $1.65. Construct a 98% confidence interval to estimate the mean hourly wage of these fast food workers.
$10.88 < µ < $11.62
A local java joint claims that its drip coffee has a caffeine content of 140 mg per 8-oz cup. To test this claim, you find 42 8-oz cups and calculate the mean caffeine content to be 146 mg with a standard deviation of 22 mg. At α = 0.05, what is the conclusion for this test?
There is not enough evidence to warrant rejection of the claim that the caffeine content is 140 mg. i.e the java joint is probably telling the truth about the caffeine content.
Sample data in the textbook suggest that for the body temperatures (in degrees Fahrenheit) of normal healthy adults, x-bar= 98.20°F and s = 0.62°F, and the temperatures have a normal distribution. If 20 people are randomly selected, find the probability that their mean body temperature is greater than 98.30°F.
0.2354
The population standard deviation of the mean weight of rat terrier dogs is 2.1 pounds. About what sample size is needed for a 95% confidence interval to estimate the true mean weight of rat terrier dogs to be within a margin of error of 1.5 pounds?
8
A football coach randomly selected ten players and timed how long each player took to perform a certain drill. (Assume drill times are approximately normal.) The times (in minutes) were:
7.5 10.3 9.7 8.0 11.8 7.0 12.9 11.1 10.5 12.4
Calculate a 97% confidence interval for the mean time for all players.
We are 97% confident that the mean time for all players to complete this drill is between 8.44 mins and 11.80 mins.
An environmental focus group claims that more than 30% of US consumers have stopped buying a certain product because the manufacturing of the product pollutes the environment. To test this, you randomly select 1050 US consumers and find that 32% have stopped buying this product due to pollution concerns. At α = 0.10, what is the conclusion for this test?
There is enough evidence to support the claim that more than 30% of consumers have stopped buying this product due to pollution concerns.
What weight separates the lightest 99.5% of men from the heaviest 0.5%? Again assume that weights of men are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.
246.7 lbs
Last year, 35% of people in a town said they would vote for reelection of the mayor. If it is reasonable to believe that this proportion is at least this high now, what is the minimum sample size needed for a 99% confidence interval, and to have a margin of error of 5%?
604