Question 1

Which of the following is a requirement for testing a claim about a population mean when the population standard deviation is not known?

Accepted Answer

The sample must be a simple random sample.

Question 2

When testing a claim about a population mean with an unknown population standard deviation, which distribution should be used to find critical values?

Accepted Answer

Student t distribution

Question 3

Given a sample size $$n = 12$$, sample mean $$\overline{x} = 6.833$$, and sample standard deviation $$s = 1.592$$, what are the degrees of freedom for the t-test?

Accepted Answer

$$df = 11$$

Question 4

A researcher wants to test if the mean body temperature is different from 98.6°F using a sample of $$n = 106$$, $$\overline{x} = 98.20$$, and $$s = 0.62. $$Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu = 98.6$$

Question 5

Why is it common to consider the normality requirement satisfied if $$n \u003e 30$$?

Accepted Answer

Because the central limit theorem states that the distribution of sample means will approximate normality for large samples.

Question 6

Which of the following is NOT a recommended approach if the exact degrees of freedom are not found in the t-table?

Accepted Answer

Use the next higher number of degrees of freedom in the table.

Question 7

Calculate the test statistic for the following scenario: $$n = 12$$, $$\overline{x} = 6.833$$, $$s = 1.592$$, testing $$H_0$$: \mu = 7$$.

Accepted Answer

$$t = \frac{6.833 - 7}{1.592 / \sqrt{12}}$$

Question 8

In the context of hypothesis testing, what does the P-value represent?

Accepted Answer

The probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.

Question 9

Suppose you are testing $$H_0$$: \mu = 7$$ against H_1$: \mu \u003c 7$$ with $$\alpha = 0.05. If $$your calculated P-value is 0.03, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is sufficient evidence to support $$\mu \u003c 7.$$

Question 10

Why is the 'σ known' approach for testing population means now considered obsolete?

Accepted Answer

Because modern technology allows us to use the t-distribution even when σ is unknown.

Question 11

A sample of $$n = 106$$ body temperatures has $$\overline{x} = 98.20$$ and $$s = 0.62. $$What is the standard error of the mean?

Accepted Answer

$$\frac{0.62}{\sqrt{106}}$$

Question 12

Which of the following best describes the central limit theorem?

Accepted Answer

For large sample sizes, the distribution of sample means approaches a normal distribution, regardless of the population's distribution.

Question 13

If a population distribution is extremely far from normal, what should you consider when determining sample size for hypothesis testing?

Accepted Answer

A much larger sample size than 30 may be needed for the central limit theorem to apply.

Question 14

Which of the following is a correct interpretation of a significance level $$\alpha = 0.05$$?

Accepted Answer

There is a 5% risk of rejecting the null hypothesis when it is actually true.

Question 15

A sample of sleep times yields $$n = 12$$, $$\overline{x} = 6.833$$, $$s = 1.592. $$What is the value of the standard error?

Accepted Answer

$$\frac{1.592}{\sqrt{12}}$$

Question 16

Which of the following scenarios would require the use of the t-distribution rather than the z-distribution?

Accepted Answer

The population standard deviation is unknown and the sample size is 25.

Question 17

If you are testing $$H_0$$: \mu = 98.6$$ using a sample with n = 106$, $$\overline{x} = 98.20$$, s = 0.62$, what is the formula for the test statistic?

Accepted Answer

$$t = \frac{98.20 - 98.6}{0.62 / \sqrt{106}}$$

Hypothesis Testing for Population Mean (σ Unknown) – Step-by-Step Guidance

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