Proportion Refreshers
You want to estimate the proportion of your classmates that send more than 50 texts a day. Should you run a test or find a confidence interval to answer this question?
To estimate a number, find a confidence interval.
For what variables do we use the t-distribution: Means or Proportions?
Means
The part of your hypothesis that always has an equal sign
Null
How do you check the large enough condition for inference with proportions?
Check np and nq. If the null hypothesis proportion would predict 10 successes and 10 failures with the given sample size then it is large enough.
People applying for a driver's license In California usually need to take a multiple choice test. An administrator takes an SRS of 15 test results and find that the times are strongly skewed to the left with a mean of x=14.2 minutes. Which conditions for constructing a t interval have been met?
Random and 10%
The normal condition when n isn't greater than or equal to 30 or from a normal population
Graph of sample data looks roughly symmetric nd unimodal
Calculate the standard deviation of p hat if:
p = 0.34
n = 400
.0237
Camila is curious about the average length of the female blue whales. She takes a random sample of 4 female blue whales. Their average recorded length is x=78 and their standard deviation is s=10. The distribution of lengths in the sample is roughly symmetric with no obvious outliers.
Based on this sample, create a 95% confidence interval for the mean length (in meters) of female blue whales
(62.09,93.91)
Pepsi claims that Bubly has 12.0 oz in each can and you suspect that number is too high. You take a random sample of 65 Bubly cans, and measure the amount of water in each can. You find that the average of the cans in your sample is 11.95 oz with a deviation of .2 ounces. Find the p-value for this question.
p = .024
In a representative sample of 100 people, 53% approve of the president. Find a 95% confidence interval to report the data.
A 1-prop z-int with x=53 n=100 and CL = .95 gives a confidence interval between 43% and 63% approval.
A random sample of 22 people resulted in a 87% confidence interval of (5.8, 12.2). What was the sample mean and margin of error?
x-bar = 9
ME = 3.2
The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year’s female graduates from a large local high school differs from the national average. You measure an SRS of 48 female graduates and find that x¯=63.5 inches and sx=3.7 inches . Make an appropriate conclusion
ts = -1.31, p-value = .196, there is not enough evidence to suggest this class is different than the population.
What is the margin of error for the confidence interval (0.55, 0.72)
.085
Which of the following would make the margin of error decrease?
a) Increasing sample size
b) Decreasing sample size
c) Increasing Confidence Level
d) Decreasing Confidence Level
e) Decrease sample mean
f) Decrease sample sd
a, d, f
The principal of a large high school wants to know if students spend more than 1 hour doing homework per night, on average. To investigate, he surveys a random sample of 100 students and use the results to test the following hypotheses:
H0: μ = 1
Ha: μ > 1
where μ is the mean amount of homework done per night for all the students at the school.
Describe a Type II error in the context of this study.
The principal doesn't find convincing evidence that students spend more than an hour on homework per night on average, but they do spend more than an hour per night on average.