Question 1

A certain brand of flood lamps has a lifetime that is normally distributed with a mean of 3750 hours and a standard deviation of 300 hours. The manufacturer does not want more than 2% of the lamps to burn out before the advertised lifetime. Which of the following StatCrunch > Calculators > Normal instructions correctly finds the advertised lifetime so that only 2% of lamps burn out before this time?

Accepted Answer

Mean: 3750, Std. Dev.: 300, P(X ≤ 3133.8753) = 0.02

Question 2

The weight of a randomly selected container of yogurt coming off an assembly line is Normally distributed with mean $\mu = 6.20$ oz. and standard deviation $\sigma = 0.10$ oz. What is the probability that a randomly selected yogurt container will weigh less than 6 oz.?

Accepted Answer

$0.0228$

Question 3

Which of the following is NOT a characteristic of the normal probability distribution?

Accepted Answer

The distribution is symmetrical around $\sigma$ (sigma)

Question 4

If the standard error of the sampling distribution of the sample proportion is $0.0337$ for samples of size $n = 200$, what is the population proportion $p$?

Accepted Answer

$p = 0.25$ or $p = 0.75$

Question 5

Random samples of size $n = 49$ are taken from an infinite population whose mean is $\mu = 300$ and standard deviation is $\sigma = 21$. What are the mean and standard error of the sample mean, respectively?

Accepted Answer

Mean: $300$, Standard Error: $3$

Question 6

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of $3.2$ pounds and standard deviation of $0.8$ pounds. If a sample of $25$ fish yields a mean of $3.6$ pounds, what is the Z-score for this sample mean?

Accepted Answer

$2.5$

Question 7

Which of the following statements about the Student’s t distribution is FALSE?

Accepted Answer

As the degrees of freedom get smaller, the t-distribution’s standard deviation gets smaller.

Question 8

A sample of size $n = 200$ will be taken at random from an infinite population. Given that the population proportion is $p = 0.60$, the probability that the sample proportion will be greater than $0.58$ is closest to:

Accepted Answer

$0.719$

Question 9

Suppose you wish to calculate a $95\%$ confidence interval estimate of the population mean using a sample size of $n = 30$. The population standard deviation is not known and will be estimated with the sample standard deviation. What critical number is used to calculate the margin of error?

Accepted Answer

$2.042$

Question 10

A $95\%$ confidence interval for a population mean is the range of values $(25.1, 28.3)$. What is the appropriate conclusion?

Accepted Answer

Since $95\%$ of all confidence intervals calculated this way capture the population mean, we are $95\%$ confident that this interval contains the true value of $\mu$.

Question 11

In hypothesis testing, the point that separates sample outcomes that 'Reject $H_0$' from those that 'Do Not Reject $H_0$' is called:

Accepted Answer

the critical point

Question 12

To ensure that a hypothesis test has a low risk of committing a Type I error, we choose:

Accepted Answer

a small significance level

Question 13

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ________; hence the power of the test will ________.

Accepted Answer

Decrease; increase

Question 14

Which of the following power curves correctly represents a one-sided hypothesis test for $H_A: p > 0.65$ at $\alpha = 0.01$ and sample size $n = 400$?

Accepted Answer

The third image (power curve rising to the right, labeled 'Alternative: >')

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