Q: A sample of 100 light bulbs has a mean lifetime of 1200 hours with a standard deviation of 100 hours. Construct a 95% confidence interval for the mean lifetime. Which of the following is correct?

$$1200 \pm 1.96 \times \frac{100}{\sqrt{100}}$$

Question 1

Which of the following best describes the purpose of hypothesis testing in statistics?

Accepted Answer

To determine if there is enough evidence in a sample to support a specific claim about a population.

Question 2

A researcher wants to compare the average test scores of two independent groups. Which statistical test should they use?

Accepted Answer

Two-sample t-test

Question 3

Suppose you are testing the claim that the mean weight of a certain species of fish is 10 kg. You collect a sample and calculate a test statistic. If your significance level is $$\alpha = 0.05$$ and your p-value is $$0.03$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 4

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 5

A medical researcher is interested in whether a new drug lowers blood pressure more effectively than the current standard. Which is the appropriate null hypothesis?

Accepted Answer

$$H_0$$: \mu_{new} = \mu_{standard}$$

Question 6

Which of the following is a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 7

A sample of 100 light bulbs has a mean lifetime of 1200 hours with a standard deviation of 100 hours. Construct a 95% confidence interval for the mean lifetime. Which of the following is correct?

Accepted Answer

$$1200 \pm 1.96 	imes \frac{100}{\sqrt{100}}$$

Question 8

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 9

A company claims that at least 80% of its products pass quality control. A random sample of 200 products shows that 150 pass. What is the sample proportion?

Accepted Answer

$$\frac{150}{200} = 0.75$$

Question 10

Which of the following is the correct formula for the test statistic in a one-sample z-test for a population mean?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$

Question 11

A researcher conducts a two-tailed test at the $$\alpha = 0.01$$ significance level. Which of the following p-values would lead to rejecting the null hypothesis?

Accepted Answer

0.009

Question 12

Which of the following scenarios requires the use of a paired t-test?

Accepted Answer

Comparing pre-test and post-test scores of the same students.

Question 13

If the 95% confidence interval for a population mean is $$(50, 60)$$, which of the following statements is correct?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 14

Which of the following is NOT an assumption of the one-way ANOVA test?

Accepted Answer

The sample means are equal.

Question 15

A Type II error occurs when:

Accepted Answer

A false null hypothesis is not rejected.

Question 16

Which formula is used to calculate the standard error of the mean?

Accepted Answer

$$SE = \frac{s}{\sqrt{n}}$$

Question 17

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 18

Which of the following is the correct formula for the sample variance?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 19

A researcher wants to test if a coin is fair. She flips it 100 times and gets 60 heads. Which test should she use?

Accepted Answer

One-sample z-test for proportions

Question 20

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

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

MATH 1127 Statistics Course Syllabus and Schedule Overview

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