Q: Which of the following statements accurately describes the null hypothesis? Select all that apply.
- The null hypothesis typically assumes that observed data does not occur by chance.
- The null hypothesis is accepted as true only if there is convincing evidence for it.
- The null hypothesis is assumed to be true unless there is convincing evidence to the contrary.
- The null hypothesis typically assumes that observed data occurs by chance.
Explanation: Within the context of statistical hypothesis testing, this phrase makes an accurate description of the null hypothesis. It assumes that there is no substantial impact or association in the population unless there is evidence that leads one to believe differently. This assertion is correct because the null hypothesis often presumes that any observed difference or connection between variables is the result of random chance rather than a genuine effect or link.
Q: What term describes the probability of rejecting the null hypothesis
when it is true?
- P-value
- Confidence interval
- Alternative hypothesis
- Significance level
Explanation: In statistical analysis, the significance level, which is often represented by the symbol α, represents the chance of making a Type I mistake. This error happens when the null hypothesis is rejected when it is really true. It denotes the point at which the null hypothesis is seen as being sufficiently improbable to be discarded in favor of the alternative hypothesis after reaching this threshold.
Q: A data professional conducts a hypothesis test. They fail to reject
the null hypothesis. What statement best describes their conclusion?
- Their significance level is greater than their p-value
- Their confidence level is greater than their p-value
- Their p-value is greater than their significance level.
- Their p-value is greater than their confidence level
Explanation: This is the point at which the null hypothesis is considered to be true. It is common practice to employ significance values of 0.05 (five percent) or 0.01 (one percent). Under the premise that the null hypothesis is correct, the p-value is the likelihood of receiving outcomes that are as severe as the observed results (or even more extreme). If the p-value is higher than the designated significance threshold (for example, 0.05), this indicates that there is insufficient evidence to reject the null hypothesis.
Q: A data professional conducts a hypothesis test. When they draw their
conclusion, they commit a type I error. Which of the following statements
describe their error? Select all that apply.
- They fail to reject a null hypothesis that is actually false.
- They conclude their result occurred by chance when in fact it is statistically significant.
- They reject a null hypothesis that is actually true.
- They conclude their result is statistically significant when in fact it occurred by chance.
Explanation: This sentence provides an accurate description of a Type I mistake." When a data professional rejects the null hypothesis (concludes that there is an effect or link) when, in reality, the null hypothesis is true (that there is no impact or relationship) in the population, this is an example of a Type I mistake. In addition, a Type I mistake is described in this sentence. This indicates that the data professional has made an erroneous conclusion, namely that their observed result is statistically significant (rejecting the null hypothesis), whereas, in fact, the observed result is due to random chance fluctuation.
Q: A data professional at an emergency response center conducts a
hypothesis test to identify optimal ambulance routes. They just found the
p-value. What should they do next?
- Choose the significance level
- State the alternative hypothesis
- State the null hypothesis
- Reject or fail to reject the null hypothesis
Explanation: When the data give sufficient evidence to reject the null hypothesis, the significance level is the threshold that decides whether or not the result is significant. It is common practice to employ significance values of 0.05 (five percent) or 0.01 (one percent). Determine the test statistic (such as the t-statistic, z-score, or F-statistic) based on the data, and then carry out the hypothesis test. Under the premise that the null hypothesis is correct, the p-value is the likelihood of receiving outcomes that are as severe as the observed results (or even more extreme).
Q: A data professional conducts a hypothesis test. They choose a
significance level of 10%. They calculate a p-value of 12.4%. What conclusion
should they draw?
- Reject the alternative hypothesis.
- Fail to reject the null hypothesis.
- Fail to reject the alternative hypothesis.
- Reject the null hypothesis
Explanation: The threshold that is used to decide whether it is appropriate to reject the null hypothesis is referred to as the significance level (α). The significance level in this instance is 10%, which indicates that the data professional is ready to tolerate a 10% risk of mistakenly rejecting the null hypothesis (also known as a Type I error). Under the premise that the null hypothesis is correct, the p-value of 12.4% reflects the likelihood of witnessing the data (or more extreme findings) if the null hypothesis is correct.
Q: A data professional is conducting a two-sample t-test. What does
their alternative hypothesis state?
- There is no difference between two population means.
- There is a difference between two population proportions.
- There is no difference between two population proportions.
- There is a difference between two population means.
Explanation: This indicates that the data professional is determining whether or not there is evidence to support the hypothesis that the means of two distinct populations are distinct from one another. On the other hand, the null hypothesis would assert that there is no difference between the two population means (the two population means).
Q: A data professional conducts a hypothesis test to compare the mean
annual sales of two different restaurants in the same restaurant chain. They
write the following code:
scipy.stats.ttest_ind(a=530,
b=550, equal_var=FALSE)
What does the argument equal_var=FALSE refer to?
- Whether or not the population variance of the two samples is assumed to be equal
- Significance level
- P-value
- Observations from the first sample
Explanation: When doing a t-test, it is necessary to make an assumption on the variance (spread) of the data within each group that is being compared (in this particular instance, the mean yearly sales of two separate restaurants). This function makes the assumption that the variances of the two populations (or samples) are comparable when equal_var is set to True. Alternatively referred to as the Student's t-test, this is also known as the equal variance t-test. Consequently, the test ought not to presume that the two populations (or samples) have similar variances, as this shows. This variant of the t-test is known as Welch's t-test, and it does not assume that the variances are equal. Instead, it changes the degrees of freedom under the variances.
Q: Which of the following statements accurately describe the null
hypothesis? Select all that apply.
- The alternative hypothesis typically assumes that observed data occurs by chance.
- The null hypothesis typically assumes that observed data does not occur by chance.
- The null hypothesis typically assumes that observed data occurs by chance.
- The alternative hypothesis typically assumes that observed data does not occur by chance.
Q: To draw a conclusion about the null hypothesis, what two concepts
are compared?
- Confidence level and significance level
- P-value and significance level
- P-value and alternative hypothesis
- Alternative hypothesis and significance level
Explanation: Under the premise that the null hypothesis is correct, the p-value is the likelihood of receiving outcomes that are as severe as the observed results (or even more extreme). It provides a numerical representation of the strength of the evidence that contradicts the null hypothesis.To determine whether to reject the null hypothesis, the significance level, which is often represented by the symbol α, serves as the threshold. It is a measure of the likelihood of making a Type I mistake, which is defined as saying that the null hypothesis is incorrect when in fact it is correct.
Q: A data professional conducts a hypothesis test to compare the mean
annual sales of two different restaurants in the same restaurant chain. They
write the following code:
scipy.stats.ttest_ind(a=530,
b=550, equal_var=FALSE)
What does the argument a=530 refer to?
- Whether or not the population variance of the two samples is assumed to be equal
- Significance level
- P-value
- Observations from the first sample (CORRECT)
Q: What is the term for the arbitrary threshold determining whether an
observed difference between groups occurred by chance?
- P-value
- Maximum likelihood
- Statistical significance
- Confidence level
Explanation: This idea pertains to the question of whether or not a previously observed outcome is very improbable to have been the product of random chance alone. It is calculated by comparing the data that has been seen to a threshold that is known as the significance level, which is often represented by the symbol α. The result is regarded to be statistically significant if the p-value, which is the probability value associated with the test statistic, is either lower than or equal to the significance threshold. Consequently, this indicates that there is a enough amount of evidence to reject the null hypothesis in favor of the alternative hypothesis.
Q: A data professional conducts a hypothesis test. When they draw their
conclusion, they fail to reject a null hypothesis, which is actually false.
What type of error do they commit?
- Type I
- Type III
- Type II
- Type IV
Explanation: In this particular instance, the mistake that was made is a Type II error. This can take place when the data professional fails to reject a null hypothesis that is demonstrably incorrect.
Q: A data professional conducts a hypothesis test. They choose a
significance level of 5%. They calculate a p-value of 3.3%. What conclusion
should they draw?
- Reject the alternative hypothesis.
- Fail to reject the null hypothesis.
- Reject the null hypothesis.
- Fail to reject the alternative hypothesis.
Explanation: If the p-value is lower than or equal to the significance threshold (α), which is commonly 5% or 0.05, then we reject the null hypothesis based on the statistical analysis.If the p-value exceeds the significance threshold (α), it is not possible to reject the null hypothesis by statistical analysis.
Q: In a one-sample hypothesis test of the mean, what are the typical
options for the alternative hypothesis? Select all that apply.
- The population mean is equal to an observed value.
- The population mean is greater than an observed value.
- The population mean is less than an observed value.
- The population mean is not equal to an observed value.
Explanation: The purpose of this is to determine whether or not the mean of the population is higher than a certain figure.The purpose of this is to determine whether or not the mean of the population is lower than a certain figure.The purpose of this is to determine whether or not the mean of the population is different (exceeding or falling short of) a certain figure.
Q: A data professional conducts a hypothesis test. They choose a
significance level of 1%. They calculate a p-value of 0.01%. What conclusion
should they draw?
- Fail to reject the null hypothesis.
- Reject the alternative hypothesis.
- Fail to reject the alternative hypothesis.
- Reject the null hypothesis.
Explanation: About this particular instance, the data professional computed a p-value of 0.01%, which is lower than the significance threshold of 1% required. It is for this reason that they ought to reject the null hypothesis.
Q: A data professional is conducting a hypothesis test. Their null
hypothesis states that there is no difference between two population
proportions. What type of test are they conducting?
- Two-sample z-test
- Two-sample t-test
- One-sample z-test
- One-sample t-test
Explanation: In most cases, a two-sample z-test is equivalent to the hypothesis test in which the null hypothesis asserts that there is no difference in the proportions of two populations. The purpose of this test is to assess whether or not there is a substantial difference between the proportions of two separate populations or groups that are independent of one another.
18. What does the concept of p-value refer to?
- The probability of observing results as or more extreme than those observed when the null hypothesis is true
- The probability of observing results less extreme than those observed when the null hypothesis is true
- The probability of rejecting the null hypothesis when it is false
- The probability of rejecting the null hypothesis when it is true
Explanation: The p-value is a statistical measure that assesses the strength of the evidence that contradicts the null hypothesis. This description encapsulates the core of what the p-value signifies about hypothesis testing. Additionally, it provides an indication of the chance of receiving test outcomes (or more severe results) if the null hypothesis is correct.
19. When would a data professional reject the null hypothesis?
- When their test statistic is less than their p-value
- When their significance level is less than their p-value
- When their p-value is less than their test statistic
- When their p-value is less than their significance level
Explanation: A comparison of the estimated p-value with the selected significance level (α) is the basis for the decision to reject the null hypothesis in the process of hypothesis testing. Furthermore, if the p-value is less than the significance threshold α, it signifies that the observed data is very improbable to have happened if the null hypothesis were to be true. We conclude that the alternative hypothesis is more likely to be correct than the null hypothesis.