# QNT 275 Week 4 Practice Connect Knowledge Check

PLDZ-7516**Description**

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Therefore, the alternative hypothesis can be written as HA: μ > 100. (Assume the population is normally distributed.)

True

False

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

True

False

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are μ = 3.5 and σ = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is

7.0

3.5

0.05

0.5

If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of with a normal distribution.

True

False

The power of a statistical test is the probability of rejecting the null hypothesis when it is false.

True

False

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. What is the alternative hypothesis?

p ≤ .66

p < .66

p = .66

p > .66

The t distribution always has n degrees of freedom.

True

False

It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 23 download times are selected, describe the shape of the sampling distribution and how it was determined.

skewed; the original population is not a normal distribution

cannot be determined with the information that is given

normal; the original population is normal

normal; size of sample meets the Central Limit Theorem requirement

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis.

p > .66

p ≠ .66

p ≤ .66

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. From the 900 respondents, how many indicated that they would not vote for the current governor or indicated that they were undecided?

405

400

450

495

It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, calculate the mean of the sampling distribution of the sampling mean.

0.3

0.05

0.15

0.9

For a given hypothesis test, if we do not reject H0, and H0 is true,

no error has been committed.

a Type I error has been committed.

a Type II error has been committed.

a Type III error has been committed.

According to the Central Limit Theorem, if a sample size is at least _____, then for most sampled populations, we can conclude that the sample means are approximately normal.

50

25

20

30

If the sampled population distribution is skewed, then in most cases the sampling distribution of the mean can be approximated by the normal distribution if the sample size n is at least 30.

True

False

The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

True

False

A(n) _____________ hypothesis is the statement that is being tested. It usually represents the status quo, and it is not rejected unless there is convincing sample evidence that it is false.

true

research

alternative

null

The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the mean of the sampling distribution of the sample mean.

0.8

5.2

0.08

0.018

If a population distribution is known to be normal, then it follows that

None of the other choices is correct.

the sample mean must equal the population mean.

the sample mean must equal the population mean, the sample mean must equal the population mean for large samples, and the sample standard deviation must equal the population standard deviation.

the sample standard deviation must equal the population standard deviation.

the sample mean must equal the population mean for large samples.

If p = .8 and n = 50, then we can conclude that the sampling distribution of is approximately a normal distribution.

True

False

As the sample size increases, the standard deviation of the sampling distribution increases.

True

False

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