MCQs

Question 1

Which of the following conditions must be met for a random variable to be considered binomially
distributed? (3p)

a) The Number of trials is infinite.

b) Each trial is dependent on the outcome of the previous trial.

c) Each trial results in one of two possible outcomes, and the probability of success remains constant.

d) The trials can result in multiple outcomes, not just two.

e) The probability of success may change after each trial.

Answer 1

c) Each trial results in one of two possible outcomes, and the probability of success remains constant.

Question 2

Which of the following statements is true regarding continuous random variables?
a) They can take on only a finite number of values.

b) They are always normally distributed.

c) Continuous random variables have a mean that is always equal to zero.

d) The probability of a continuous random variable taking on any single, specific value is zero.

e) None of the above statements are correct.

Answer 2

d) The probability of a continuous random variable taking on any single, specific value is zero.

Question 3

What does a p-value of 0.02 represent in hypothesis testing?

a) There is a 2% probability of rejecting the null hypothesis when it is true.

b) There is a 2% probability that the alternative hypothesis is true.

c) There is a 2% probability of obtaining the observed test statistic, or more extreme results, assuming the null hypothesis is correct.

d) The probability of the observed test statistic occurring under the null hypothesis is 2%.

e) There is a 98% chance that the alternative hypothesis is true.

Answer 3

c) There is a 2% probability of obtaining the observed test statistic, or more extreme results, assuming the null hypothesis is correct.

Question 4

Under which of the following conditions does the confidence interval for a population
parameter become larger? (3p)

a) Increasing the variability in the data.

b) Increasing the sample size.

c) Decreasing the confidence level.

d) Using a smaller critical value from the corresponding distribution.

e) None of the above statements are correct.

Answer 4

a) Increasing the variability in the data.

Question 5

or each of the following 5 statements, determine whether it is true or false.

a) In combinations, the order of selection does not matter.

b) The median should not be used when the distribution is skewed or if there
are extreme values (outliers) in the data.

c) In an independent sample design, observations are paired.

d) In a histogram, the height of each bar represents the frequency of data for one
specific outcome.

e) A random sample ensures that every member of the population has an equal chance
of selection.

Answer 5

Here are the answers:

a) True
b) False
c) False
d) True
e) True

Question 6

Which of the following is considered an ordinal scale of measurement?

a) Length in centimeters

b) Temperature in Celsius

c) Gender

d) Weight in kilograms

e) Levels of satisfaction (unsatisfied, neutral, satisfied)

Answer 6

e) Levels of satisfaction (unsatisfied, neutral, satisfied)

Question 7

What is the standard deviation of a binomial distribution with 50 trails and a probability of
success of 0.3? (4p)
a) 15
b) 10.5
c) 3.24
d) 35
e) None of the above

Answer 7

c) 3.24
the standard deviation of a binomial distribution is calculated using the formula:

𝜎=𝑛⋅𝑝⋅(1−𝑝)σ= n⋅p⋅(1−p)
(och roten ur hela)

Where:
n=50 (the number of trials)
p=0.3 (the probability of success)
1−p=0.7 (the probability of failure)

Question 8

7. Which of the following statements best describes mutually exclusive events?

a) Mutually exclusive events have a combined probability of 1.

b) Mutually exclusive events can occur simultaneously.

c) Mutually exclusive events have no outcomes in common.

d) Mutually exclusive events have identical probabilities.

e) Mutually exclusive events always have a probability of 0.

Answer 8

c) Mutually exclusive events have no outcomes in common.

Question 9

When is a histogram most appropriate for data visualization?
a) When examining the distribution of categorical data.

b) When examining the relationship between two continuous variables.

c) When examining the distribution of a continuous variable.

d) When presenting data over time.

e) None of the above alternatives (a-d) are suitable.

Answer 9

When examining the distribution of a continuous variable.

Question 10

For each of the following 5 statements, determine whether it is true or false.

a) An event is defined as a collection of sample points

b) The t-distribution is a symmetric distribution.

c) If the number of observations in the sample increases, then the variance of X increases

d) For a symmetric distribution the mean and median are equal.

e) In combinations, the order of the elements does not matter.

Answer 10

a) True
b) True
c) False
d) True
e) True

Question 11

Which of the following is NOT an assumption in ANOVA testing?
a) The variances of the populations should be equal.

b) Independence of observations.

c) The populations from which the samples were taken are normally distributed.

d) Equality of sample sizes.

e) All of the above alternatives (a-d) are assumptions of the ANOVA test.

Answer 11

d) Equality of sample sizes.

Question 12

Which of the following statements related to discrete random variables is correct?

a) Discrete random variables can take on any value within a given range.

b) Random variables following the T-distribution are discrete random variables.

c) Discrete random variables are limited to whole numbers (integers).

d) Discrete random variables can only assume distinct, separate values.

e) None of the above alternatives (a-d) are correct.

Answer 12

d) Discrete random variables can only assume distinct, separate values.

Question 12

A type of apple has a mean weight of 150 grams and a standard deviation of 20 grams. If you
randomly select samples of 50 apples, which alternative about the distribution of the sample
mean is correct? (4p)

a) The sample mean will have a standard deviation of 20 grams.

b) The sample mean will be approximately normal.

c) The sample mean will have the exact same distribution as the population.

d) The sample mean will have a mean different from 150 grams.

e) None of the above alternatives (a-d) are correct.

Answer 12

b) The sample mean will be approximately normal.

Question 13

If the p-value in a hypothesis test is 0.08, what does this value indicate about the results? (4p)
a) There is an 8% chance of obtaining the observed results, or a more extreme results, if the
null hypothesis is true.

b) There is an 8% chance that the null hypothesis is true.

c) There is an 8% chance that the alternative hypothesis is true.

d) There is an 8% chance of making a Type I error.

e) None of the above interpretations (a-d) are correct.

Answer 13

a) There is an 8% chance of obtaining the observed results, or more extreme results, if the null hypothesis is true.

Explanation:
A p-value of 0.08 indicates that, assuming the null hypothesis is true, there is an 8% probability of obtaining the observed result, or results more extreme than the one observed. The p-value is used to assess the strength of evidence against the null hypothesis.

Question 14

For each of the following 5 statements, determine whether it is true or false. No explanation is
necessary. A correct response earns 2 points, an incorrect response deducts 2 points, and
leaving the answer blank yields 0 points. The total score for these questions will never be less
than zero, even if you provide incorrect responses for all of them. Write your response on the
answer sheets provided, rather than within the exam itself. (10p)

a) In a random sample, all elements of the population have the same probability of being
selected.

b) The F-distribution is a symmetric distribution.

c) In a binomial distribution with 5 trials and a success probability of 0.2, the standard
deviation is equal to 0.8.

d) An event is a collection of sample points.
e) The 50th percentile is the same as the median.

Answer 14

a) True
b) False
c) False
d) True
e) True