For a hypothesis test of the claim that the mean amount of sleep for adults is less than 8 hours, technology output shows that the hypothesis test has power of 0.4005 of supporting the claim that u<8 hours of sleep when the actual population mean is 6.5 hours of sleep. Interpret this value of the power, then identify the value of B and interpret that value. Interpret this value of the power. O A. The chance of failing to recognize that p= 6.5 hours is not very high when in reality u=6.5 hours O B. The chance of failing to recognize that p <8 hours is not very high when in reality u=6.5 hours. OC. The chance of recognizing that p<8 hours is very high when in reality p= 6.5 hours. O D. The chance of recognizing that u<8 hours is not very high when in reality u= 6.5 hours. Identify the value of B and interpret that value. Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) OA The value B= indicates that there is a greater than 50% chance of failing to recognize that u<8 hours when reality u =6.5 hours. O B. The value B= indicates that there is a less than 50% chance of failing to recognize that u<8 hours when in reality u = 6.5 hours. OC. The value B= indicates that there is a greater than 50% chance of incorrectly recognizing that p<8 hours when reality u=8 hours. O D. The value B= indicates that there is a less than 50% chance of incorrectly recognizing that p<8 hours when in reality u=8 hours.

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For a hypothesis test of the claim that the mean amount of sleep for adults is less than 8 hours, technology output shows that the hypothesis test has power of 0.4005 of supporting the claim that μ < 8 hours of sleep when the actual population mean is 6.5 hours of sleep. Interpret this value of the power, then identify the value of β and interpret that value.

---

Interpret this value of the power:

- **A.** The chance of failing to recognize that μ = 6.5 hours is not very high when in reality μ = 6.5 hours.
- **B.** The chance of failing to recognize that μ < 8 hours is not very high when in reality μ = 6.5 hours.
- **C.** The chance of recognizing that μ < 8 hours is very high when in reality μ = 6.5 hours.
- **D.** The chance of recognizing that μ < 8 hours is not very high when in reality μ = 6.5 hours.

Identify the value of β and interpret that value. Select the correct choice below and fill in the answer box to complete your choice.

(Round to four decimal places as needed.)

- **A.** The value β = ☐ indicates that there is a greater than 50% chance of failing to recognize that μ < 8 hours when in reality μ = 6.5 hours.
- **B.** The value β = ☐ indicates that there is a less than 50% chance of failing to recognize that μ < 8 hours when in reality μ = 6.5 hours.
- **C.** The value β = ☐ indicates that there is a greater than 50% chance of incorrectly recognizing that μ < 8 hours when in reality μ = 8 hours.
- **D.** The value β = ☐ indicates that there is a less than 50% chance of incorrectly recognizing that μ < 8 hours when in reality μ = 8 hours.
Transcribed Image Text:For a hypothesis test of the claim that the mean amount of sleep for adults is less than 8 hours, technology output shows that the hypothesis test has power of 0.4005 of supporting the claim that μ < 8 hours of sleep when the actual population mean is 6.5 hours of sleep. Interpret this value of the power, then identify the value of β and interpret that value. --- Interpret this value of the power: - **A.** The chance of failing to recognize that μ = 6.5 hours is not very high when in reality μ = 6.5 hours. - **B.** The chance of failing to recognize that μ < 8 hours is not very high when in reality μ = 6.5 hours. - **C.** The chance of recognizing that μ < 8 hours is very high when in reality μ = 6.5 hours. - **D.** The chance of recognizing that μ < 8 hours is not very high when in reality μ = 6.5 hours. Identify the value of β and interpret that value. Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) - **A.** The value β = ☐ indicates that there is a greater than 50% chance of failing to recognize that μ < 8 hours when in reality μ = 6.5 hours. - **B.** The value β = ☐ indicates that there is a less than 50% chance of failing to recognize that μ < 8 hours when in reality μ = 6.5 hours. - **C.** The value β = ☐ indicates that there is a greater than 50% chance of incorrectly recognizing that μ < 8 hours when in reality μ = 8 hours. - **D.** The value β = ☐ indicates that there is a less than 50% chance of incorrectly recognizing that μ < 8 hours when in reality μ = 8 hours.
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