revision for exam 2

Question 1

the law of large numbers

Answer 1

The Law of
Large Numbers says that, as the number of
observations drawn increases, the sample
mean ҧ 𝑥 of the observed values gets closer and
closer to the mean µ of the population.

Question 2

The central limit Theorem

Answer 2

The Central Limit Theorem states
that, whatever the shape of the population
distribution, when n is “large” the sampling
distribution of the sample mean is
approximately 𝑁 𝜇,
𝜎
𝑛.

Question 3

Larger n is required when the population
distribution looks less like a Normal
distribution.
– Generally

Answer 3

n ≥ 40 is sufficiently large to use the
Normal distribution to approximate the sampling
distribution of ҧ 𝑥.

Question 4

To make m smaller, we can either

Answer 4

• Decrease our confidence 𝑧∗
• Increase our sample size 𝑛

Question 5

How can we decrease P(Type I error)?

Answer 5

Make α smaller

Question 6

How can we decrease the P(Type II error)?

Answer 6

Make α larger

Question 7

How do you interpret this p-value, i.e. what event exactly has a 27% chance of occurring?

Answer 7

If the mean purity of catalyst from the new supplier is 90, then there is a probability of 27% of obtaining a sample with mean
purity as low as observed

Question 8

Suppose that we wish to estimate the population mean grade-point average (GPA) across all UVA undergraduate
students. From a simple random sample of 50 undergraduate students, a 95% confidence interval for the population
mean GPA is (2.9, 3.6).
Which of the following is a correct interpretation of the confidence interval?

Answer 8

Answer: C: If repeated samples of size n = 50 were selected, then 95% of confidence intervals computed from these
sample means would include the population mean GPA.

Question 9

Suppose that, based on a simple random sample of n = 100 American adult men, we wish to calculate a 98%
confidence interval for the population mean height μ. For this confidence interval, the critical values ± z* could be
calculated from:

Answer 9

Answer: the 1st percentile of a N(0, 1) distribution

Question 10

What does the power of a significance test measure?

Answer 10

The probability of rejecting the null hypothesis when the alternative hypothesis is true

Question 11

in a significance test, when solving for a test statistic and determining its sampling distribution, we want to evaluate
them assuming that the alternative hypothesis is true in order to calculate a p-value

Answer 11

False

Question 12

for independent variables the standard deviaton ?

Answer 12

the standard deviation