Hypothesis Testing Mastery1

Formulate the null and alternative hypotheses for the following scenario: A researcher wants to test if the average age of students in a school is different from 20 years.

• The null hypothesis is that the average age of students in the school is less than 20 years, and the alternative hypothesis is that the average age of students in the school is greater than 20 years.

• The null hypothesis is that the average age of students in the school is equal to 25 years, and the alternative hypothesis is that the average age of students in the school is different from 20 years.

• The null hypothesis is that the average age of students in the school is equal to 20 years, and the alternative hypothesis is that the average age of students in the school is different from 20 years.

• The null hypothesis is that the average age of students in the school is equal to 20 years, and the alternative hypothesis is that the average age of students in the school is less than 20 years.

Explain the significance level in hypothesis testing and its relationship to the p-value.

• The significance level is the probability of accepting the null hypothesis when it is actually false.

• The significance level in hypothesis testing is the probability of rejecting the null hypothesis when it is actually true. The p-value is the probability of obtaining the observed data, or more extreme, when the null hypothesis is true. The significance level and the p-value are related in that the significance level is compared to the p-value to determine whether the null hypothesis should be rejected.

• The significance level and the p-value are not related and are used independently in hypothesis testing.

• The p-value is the probability of obtaining the observed data, or less extreme, when the null hypothesis is true.

Conduct a one-sample hypothesis test to determine if the average weight of a certain breed of dogs is 30 pounds. Use a significance level of 0.05.

• Conduct a one-sample t-test

• Conduct a paired t-test

• Conduct a two-sample t-test

• Conduct a chi-squared test

What are Type I and Type II errors in hypothesis testing? Provide an example of each.

• Type I error: Rejecting a good product in quality control when it is actually good. Type II error: Failing to reject a bad product in quality control when it is actually bad.

• Type I error: Failing to reject a good product in quality control when it is actually bad.

• Type II error: Rejecting a bad product in quality control when it is actually good.

• Type I error: Accepting a good product in quality control when it is actually bad.

Calculate the test statistic for a two-sample hypothesis test comparing the mean scores of two different groups of students. Group 1 has a mean score of 85 and standard deviation of 10, while Group 2 has a mean score of 78 and standard deviation of 8.

• 3.33

• 5.67

• 9.81

• 12.45

Explain the concept of critical values in hypothesis testing and how they are used to make decisions.

• Critical values are used to determine whether to reject the null hypothesis in hypothesis testing.

• Critical values are used to calculate the p-value in hypothesis testing.

• Critical values are used to determine the sample size in hypothesis testing.

• Critical values are used to determine the alternative hypothesis in hypothesis testing.

Formulate the null and alternative hypotheses for the following scenario: A company claims that their new product increases productivity by at least 20% compared to the old product.

• The null hypothesis is that the new product does not increase productivity by at least 20% compared to the old product, and the alternative hypothesis is that the new product does increase productivity by at least 20% compared to the old product.

• The null hypothesis is that the new product decreases productivity by at least 20% compared to the old product, and the alternative hypothesis is that the new product has no effect on productivity compared to the old product.

• The null hypothesis is that the new product has no effect on productivity compared to the old product, and the alternative hypothesis is that the new product decreases productivity by at least 20% compared to the old product.

• The null hypothesis is that the new product increases productivity by at least 20% compared to the old product, and the alternative hypothesis is that the new product does not increase productivity by at least 20% compared to the old product.

What is the relationship between the p-value and the level of significance in hypothesis testing?

• The p-value is compared to the level of significance to determine if the null hypothesis should be rejected or not.

• The p-value is unrelated to the level of significance

• The p-value is always higher than the level of significance

• The level of significance is used to calculate the p-value

Conduct a two-sample hypothesis test to determine if there is a difference in the average income between two cities. Use a significance level of 0.01.

• Conduct a two-sample t-test

• Conduct a one-sample t-test

• Conduct a paired t-test

• Conduct a chi-square test

Interpret the result of a hypothesis test where the p-value is 0.03 and the significance level is 0.05.

• Reject the null hypothesis

• The result is inconclusive

• Accept the null hypothesis

• The significance level is too high