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 \u003e Calculators \u003e 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 $$H_A: p \u003e 0.65 at$$ $$\alpha = 0.01$$ and sample size $$n = 400$$?

Accepted Answer

The third image (power curve rising to the right, labeled 'Alternative: \u003e')

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