Confidence Intervals
In a time use study 20 randomly selected managers were found to spend a mean time of 2.4 hours per day on paperwork. The standard deviation of the 20 scores was 1.30 hours. Construct a 98% confidence interval for the mean time spent on paperwork by all managers.
(1.66, 3.14)
Left tailed, right tailed, or two tailed?
We want to know if Westlake has a greater ACT score than the general population.
Right tailed
A hypothesis test is conducted and the p value is found to be 0.12. What can we conclude about the null hypothesis at a 10% significance level?
There is not enough evidence to reject the null hypothesis (fail to reject).
Do we conduct a significance test assuming the null hypothesis is true or false?
True
30
A random sample of 19 women results in a mean height of 63.85 inches. Other studies have shown that women’s heights are normally distributed with a standard deviation of 2.5 inches. Construct a 90% confidence interval for the mean height of all women.
(62.86, 64.85)
Left tailed, right tailed, or two tailed?
We want to know if Westlake has an ACT average that is different than the general population.
Two tailed
A news station wants to know what percent of the population will be voting for the democrat candidate in the upcoming election. A survey of 1250 people found that 476 stated they would vote for the democrat candidate.
Calculate p hat.
0.3808
Name the conditions required for hypothesis testing.
SRS and approximately normal distribution (or n>=30)
What is Ms. Lambert's master's degree in?
Earth Science Education
In a poll taken in March of 2007, Gallup asked 1006 national adults whether they were baseball fans. 36% said they were. A year previously 37% of a smaller size sample had reported being baseball fans. Find the confidence for the 2007 poll if we want 90% confidence in our estimate of the percent of national adults who are baseball fans.
(0.345, 0.395)
The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is 8 minutes. A random sample of 20 waiting times has a mean of 6.5 minutes with a standard deviation of 2.1 minutes. At α = 0.01, test to see if the mean wait time is less than 8 minutes. Assume the distribution is normally distributed.
t test
When Thanos snapped his fingers, everyone had a p=0.5 chance of disintegrating. I think that this probability was much lower for the original Avengers. Out of the 6 of them, no one got disintegrated. Can you reject the null hypothesis that there was a p=0.5 chance of each of them disintegrating with an alpha=0.05?
p=0.0071
There is significant evidence to reject the null hypothesis
Fill in the blank.
As sample size increases, the margin of error ____________.
Decreases
When is Ms. Lambert's wedding?
June 29
A researcher wants to determine the 99% confidence interval for the mean number if hours per week that adults spend doing community service. How large of a sample should the researcher select so that the estimate will be within 1 hour of the population mean? Assume that the standard deviation for hours spent per week by adults doing community service is 3.
n=35
When Thanos snapped his fingers, everyone had a p=0.5 chance of disintegrating. I think that this probability was much lower for the original Avengers. Out of the 6 of them, no one got disintegrated. Can you reject the null hypothesis that there was a p=0.5 chance of each of them disintegrating with an alpha=0.05?
1 prop z test
(proportions)
The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is 8 minutes. A random sample of 20 waiting times has a mean of 6.5 minutes with a standard deviation of 2.1 minutes. At α = 0.01, test to see if the mean wait time is less than 8 minutes. Assume the distribution is normally distributed.
p is between 0.001 and 0.0025
There is significant evidence to say that the mean wait time for a bus during rush hour is less than 8 minutes.
What kind of error/bias is covered by the margin of error?
Random sampling error
How long has Ms. Lambert been teaching?
8 years
How many American teens must be interviewed to estimate the proportion who own an iPhone within 0.02 with 99% confidence? Use 0.5 as the guess for p.
n=4148
A simple random sample of 21 chihuahua dog weights yields a sample mean of 5.6 pounds. It is known that the standard deviation of the population of all chihuahua weights is 1.8 pounds. The internet says that the mean weight of all chihuahuas is 4.6 pounds. Is there enough evidence at the 10% significance level to say that the mean is not 4.6 pounds?
z test
A simple random sample of 21 chihuahua dog weights yields a sample mean of 5.6 pounds. It is known that the standard deviation of the population of all chihuahua weights is 1.8 pounds. The internet says that the mean weight of all chihuahuas is 4.6 pounds. Is there enough evidence at the 10% significance level to say that the mean is not 4.6 pounds?
p=0.0108
There is significant evidence that the mean weight of all chihuahuas is different than 4.6 pounds.
A sample of 75 M&M bags is taken and found to have an average of 23 green pieces for bag. It is known that the population standard deviation is 3 pieces. What is the notation for the sampling distribution?
N(23, 0.35)
South Korea