Answer:
a) The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Explanation:
In hypothesis testing, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
Taking the statements one at a time
a) The assertion is that the new average time workers spent commuting to work in Verona is now less than the old average.
The null hypothesis would be there isn't enough evidence to conclude that the new average time workers spent commuting to work in Verona is now less than the old average. That is, the new average time workers spent commuting to work in Verona is now equal to or more than the old average.
The alternative hypothesis is that the new average time workers spent commuting to work in Verona is now less than the old average.
Mathematically, if μ₀ = new average time workers spent commuting to work in Verona.
The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) Although the question isn't complete,
The null hypothesis is that there isn't a significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
The alternative hypothesis is that there is significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
Mathematically, if μ₀ = Mean of whatever is being compared in the complete question
The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The claim to be proved is that the average caffeine content for coffee served in a local restaurants is higher.
The null hypothesis is that the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup. That is, the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup.
The alternative hypothesis is that average caffeine content for coffee served in a local restaurants is higher than the standard figure of 133 mg for an 8 ounce cup.
Mathematically, if μ₀ = average caffeine content for coffee served in a local restaurants.
The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The economist claims that the average yield per acre this year is different from the average yield per acre in recent years.
Hence, the null hypothesis is that there is no significant difference between the average yield per acre this year and the average yield per acre in recent years.
The alternative hypothesis is that there is significant difference between the average yield per acre this year and the average yield per acre in recent years.
Mathematically, if μ₀ = the average yield per acre this year
The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The sociologist suspects that the average age of all self-described fly fishermen is higher than 42.8 years.
Hence, the null hypothesis is that the average age of all self-described fly fishermen is not higher than 42.8 years. That is, the average age of all self-described fly fishermen is equal to less than 42.8 years.
The alternative hypothesis is that the average age of all self-described fly fishermen is higher than 42.8 years.
Mathematically, if μ₀ = average age of all self-described fly fishermen.
The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Hope this Helps!!!