Q: A manufacturer claims that the mean weight of a bag of flour is 1 kg. A quality control analyst wants to test if the mean weight is different from 1 kg. What are the correct null and alternative hypotheses?

$$H_0$$: \mu = 1$$, H_1$: \mu \neq 1$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

It is a claim about a population parameter that is assumed true until evidence suggests otherwise.

Question 2

A manufacturer claims that the mean weight of a bag of flour is 1 kg. A quality control analyst wants to test if the mean weight is different from 1 kg. What are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 1$$, H_1$: \mu 
eq 1$$

Question 3

Which of the following statements about Type I and Type II errors is correct?

Accepted Answer

A Type I error occurs when a true null hypothesis is rejected.

Question 4

Suppose a hospital administrator wants to test if the average wait time in the emergency room is more than 30 minutes. Which is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003e 30$$

Question 5

A sample of 100 manufactured bolts has a mean diameter of 29.84 mm. The population standard deviation is known to be 0.8 mm. Test the claim that the true mean diameter is 30 mm at $$\alpha = 0.05. $$What is the value of the test statistic?

Accepted Answer

$$Z = \dfrac{29.84 - 30}{0.8/\sqrt{100}} = -2.0$$

Question 6

In a two-tailed Z-test with $$\alpha = 0.05$$, what are the critical values for the test statistic?

Accepted Answer

$$-1.96$$ and $$+1.96$$

Question 7

If the p-value for a hypothesis test is 0.045 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$ because the p-value is less than $$\alpha.$$

Question 8

Which of the following factors will decrease the probability of a Type II error ($$\beta$$), all else being equal?

Accepted Answer

Increasing the difference between the hypothesized parameter and its true value

Question 9

A researcher is testing $$H_0$$: \mu = 50$$ vs. H_1$: \mu 
eq 50$$ using a sample of $$n=36$$, $$\bar{x}=48$$, $$\sigma=6$$, and $$\alpha=0.05. $$What is the value of the test statistic?

Accepted Answer

$$Z = \dfrac{48 - 50}{6/\sqrt{36}} = -2.0$$

Question 10

Which of the following best describes the p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming $$H_0 is $$true.

Question 11

A pharmaceutical company claims that its new drug reduces blood pressure by at least 10 mmHg on average. Which of the following is the correct null hypothesis for testing this claim?

Accepted Answer

$$H_0$$: \mu \geq 10$$

Question 12

If a test statistic falls within the non-rejection region, what is the correct conclusion?

Accepted Answer

Do not reject the null hypothesis.

Question 13

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

Accepted Answer

Calculate the p-value and compare it to $$\alpha.$$

Question 14

A company wants to test if the mean lifetime of its light bulbs is less than 1000 hours. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c 1000$$

Question 15

If the significance level ($$\alpha) is $$decreased from 0.05 to 0.01, what is the effect on the probability of a Type II error ($$\beta$$), all else being equal?

Accepted Answer

$$\beta$$ increases

Question 16

Which of the following statements about the power of a statistical test is correct?

Accepted Answer

The power is equal to $$1 - \beta$$, where $$\beta is $$the probability of a Type II error.

Question 17

A researcher is conducting a two-tailed Z-test at $$\alpha = 0.01. $$What is the total area of the rejection regions combined?

Accepted Answer

0.01

Question 18

Which of the following is a correct interpretation of a confidence level of 95% in hypothesis testing?

Accepted Answer

If the null hypothesis is true, there is a 95% probability that we will not reject it.

Fundamentals of Hypothesis Testing: One-Sample Tests (Business Calculus Context)

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