State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μο and write to : μ analogous expression for Ha) Ao and the appropriate a. The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now
b. The mean salary for all men in a certain profession is $58,291. A special interest
c. The accepted figure for the caffeine content of an 8-ounce cup of coffee is 133 mg. A dietitian believes that the average for coffee served in a local restaurants is higher
d. The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year.
e. An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.

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

Step-by-step 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!!!

step-by-step explanation:

idk the answer i want to say 10 but then it would be equal so try 9 but then yeah so yeah we love edgen