Problem

Match the alternative hypothesis shown below with its graph to the right Then state the null hypothesis and sketch its graph \[ \mathrm{H}_{\mathrm{a}}: \sigma>5 \] Match the alternative hypothesis to its graph. Choose the correct graph below. A. B. c. State the null hypothesis

Solution

Step 1 :The alternative hypothesis is given as Ha: σ > 5. This is a one-tailed test where we are testing if the standard deviation is greater than 5. The graph for this hypothesis would show a normal distribution with the tail on the right side, indicating that we are looking for values greater than 5.

Step 2 :The null hypothesis is the statement that the parameter being tested equals the specified value. In this case, since the alternative hypothesis is that the standard deviation is greater than 5, the null hypothesis would be that the standard deviation is less than or equal to 5.

Step 3 :The graph for the alternative hypothesis Ha: σ > 5 would be a normal distribution with the tail on the right side. The null hypothesis would be H0: σ ≤ 5. The graph for the null hypothesis would be a normal distribution with the tail on the left side.

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