Question 1

Which of the following statements best describes the Central Limit Theorem (CLT)?

Accepted Answer

The CLT states that the distribution of sample means becomes approximately normal as the sample size increases, regardless of the shape of the population distribution.

Question 2

A physician wants to test if the average fasting blood glucose in Malaysia is different from the reference value of 85 mg/dL. Which statistical approach should be used?

Accepted Answer

A one-sample t-test comparing the sample mean to 85 mg/dL.

Question 3

Which of the following is TRUE about the p-value in hypothesis testing?

Accepted Answer

It is the probability of obtaining a test statistic as extreme as the observed, assuming the null hypothesis is true.

Question 4

In a hypothesis test, what does an alpha level of 0.05 represent?

Accepted Answer

The probability of rejecting the null hypothesis when it is true (Type I error).

Question 5

You are comparing the mean blood pressure between males and females. Which formula would you use to calculate the confidence interval for the difference of two means (assuming large sample sizes and known variances)?

Accepted Answer

$$ (\overline{X}_1 - \overline{X}_2) \pm Z_{\alpha} \sqrt{\frac{\$$sigma_1$$^2}{n_1$} + \frac{\$$sigma_2$$^2}{n_2$}} $$

Question 6

Which of the following is a key assumption for using a parametric test to compare two means using a Z-test?

Accepted Answer

The data points should be independent and the sample size should be greater than 30.

Question 7

A researcher wants to test if drinking alkaline water reduces the chance of cancer compared to tap water. Which hypothesis test is most appropriate?

Accepted Answer

A test comparing proportions between two independent groups.

Question 8

Which of the following best describes a Type II error in hypothesis testing?

Accepted Answer

Failing to reject the null hypothesis when it is false.

Question 9

If the confidence intervals of two groups do not overlap, what can you conclude?

Accepted Answer

The groups are most likely significantly different from each other.

Question 10

Which formula is used to calculate the confidence interval for a single sample mean when the sample size is less than 30?

Accepted Answer

$$ \overline{X} \pm t_{\alpha} SE $$

Question 11

Which of the following scenarios is most appropriate for a paired t-test?

Accepted Answer

Comparing the level of understanding before and after attending a statistics class in the same students.

Question 12

What is the correct null hypothesis for a two-tailed test comparing a sample mean to a population mean?

Accepted Answer

$$ H_0$: \mu = \mu_0$ $$

Question 13

Which of the following is NOT a requirement for using a Z-test to compare two means?

Accepted Answer

The data must be paired.

Question 14

A student measures the blood glucose of 100 individuals and finds a mean of 85 mg/dL and a standard deviation of 18.2 mg/dL. What is the 99% confidence interval for the mean?

Accepted Answer

$$ 85 \pm 2.576 	imes \frac{18.2}{10} $$

Question 15

Which of the following is a characteristic of nonparametric tests?

Accepted Answer

They do not assume any specific distribution for the data.

Question 16

When comparing two means with small sample sizes (n \u003c 30) and assuming equal variances, which formula should be used for the standard error?

Accepted Answer

$$ Sp \sqrt{\frac{1}{n_1$} + \frac{1}{n_2$}} $$

Question 17

Which of the following is TRUE regarding the relationship between hypothesis testing and confidence intervals?

Accepted Answer

If the confidence intervals of two groups do not overlap, they are most likely significantly different.

Question 18

Which of the following is a correct interpretation of a 95% confidence interval for a mean?

Accepted Answer

There is a 95% probability that the population mean falls within the interval calculated from the sample.

Parametric and Nonparametric Hypothesis Testing, Central Limit Theorem, and Confidence Intervals

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