QM 215 - Reading assignment three

Which one of the following is NOT a step we use when formulating the null and alternative hypotheses?

Calculate the value of the sample statistic.

Which of the following is NOT a step in the p-value approach to hypothesis testing?

Graph the distribution of the sample data.

The alternative hypothesis for a one-sided test looks like:

HA: μ < μ0

The alternative hypothesis for a two-sided test for a population mean would be denoted as

HA: μ ≠ μ0

Hypothesis testing enables us to determine if the collected ______ data is inconsistent with what is stated in the null hypothesis.

Sample

We always use __________ evidence and the chosen significance level α to conduct hypothesis tests.

Sample

Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are

categorical

We use the alternative hypothesis as a vehicle to establish something

new

Most researchers and practitioners favor the ___ -value approach

p

A Type I error occurs when we __________ the null hypothesis when it is true.

reject

A Type I error occurs when we...

reject the null hypothesis when it is actually true

The null hypothesis in a hypothesis test refers to

the default state of nature

When performing a hypothesis test on μ when σ is known, H0 can never be rejected if

z ≥ 0 for a left-tailed test.

An auditor for a small business wants to test the assumption that the mean value of all accounts receivable differs from $550. She takes a sample of 40 accounts and calculates the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are

H0: μ = $550 and HA: μ ≠ $550

An auditor for a small business wants to determine whether the mean value of all accounts receivable is less than $550. She takes a sample of 40 and computes the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are

H0: μ ≥ 550 and HA: μ < 550

In a hypothesis test, μ0 and p0 are hypothesized values of the ________ mean and the ______ proportion, respectively.

Population : Population

The optimal choice of α and β depends on the ______ relative of these two types of errors.

cost

Our goal in hypothesis testing is to determine if the _________ hypothesis can be rejected.

null

If the population standard deviation is unknown, it can be estimated by using ______.

s

In general, we follow three steps when formulating the competing hypotheses. Place these steps in the correct sequence.

1. Identify the population Parameter of interest 2. Determine weather its a one-tailed or two-tailed tests. 3. Include some form of equality sign in the null hypothesis

The _________ _____________ approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand.

Critical : Value

The p-value is the likelihood of obtaining a sample mean that is at least as _____________ as the one derived from the given sample, under the assumption that the null hypothesis is true as an equality.

Extreme

Hypothesis testing is analogous to a criminal court of law where someone is ________ until proven ________

Innocent ; Guilty

It is not sufficient to end the analysis with a conclusion that you reject the null hypothesis or you do not reject the null hypothesis. You must ______ the results.

Interpret

We reject H0 if the p-value is _______ _______ alpha.

Less than

The test statistic when the population standard deviation is know is z = x−μ0σ/√n�-μ0σ/�. This formula is valid only if X� follows a ______ distribution.

Normal

In order to implement an hypothesis test, it is essential that X� is ___________ distributed.

Normally

The expected value of the sampling distribution of P� is the

Population proportion

True or false: Consider the following competing hypotheses: H0: μ = 150 versus HA: μ ≠ 150. If a 95% confidence interval is [100, 200], then we cannot reject the null hypothesis at the 5% significance level.

True

True or false: For a given sample size n, a Type I error can only be reduced at the expense of a higher Type II error.

True

True or false: In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.

True

Not rejecting the null hypothesis when the null hypothesis is false

Type II error

An important final conclusion to a statistical test is to...

clearly interpret the results in terms of the initial claim.

Not rejecting a true null hypothesis

correct decision

Consider the following competing hypotheses: H0: μ = 10 versus HA: μ ≠ 10. If a 95% confidence interval is [8.25, 11.55], then at the 5% significance level we

do not reject the null hypothesis and conclude that the population mean does not significantly differ from 10.

The p-value approach to hypothesis testing has __________ steps.

four

We can generally reduce both Type I and Type II errors simultaneously by...

increasing the sample size.

If we reject the null hypothesis when it is actually false we have committed..

no error.

A binomial distribution can be approximated by a __________ distribution for large sample sizes.

normal

The normal distribution approximation for a binomial distribution is valid when

np ≥ 5 and n(1 - p) ≥ 5

When performing a hypothesis test on μ, the p-value is defined as the

observed probability of making a Type I error.

As a point estimate of the population proportion, we calculate ______.

p hat

If the chosen significance level is α = 0.05, then there is a 5% chance of

rejecting a true null hypothesis.

The critical value approach specifies a region of values, called the ______. If the test statistic falls into this region, we reject the ______.

rejection region, null hypothesis

When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a

right-tailed test.

We would conduct a hypothesis test to determine whether or not

sample evidence contradicts H0.

The p-value is calculated assuming the

the null hypothesis is true

For an alternative hypothesis of HA: μ > μ0, we might possibly reject the null hypothesis if

the population mean is greater than μ0.

A Type I error is commonly denoted as:

α (alpha)

True or false: The alternative hypothesis always states the opposite of the null hypothesis.

True

True or false: The optimal values of Type I and Type II errors require a compromise in balancing the costs of each type of error.

True

True or false: We choose a value for α before conducting a hypothesis test.

True