Question

For a bypohess lest of the elsin mat the mean amoint of shep for adues is less than 7 houn, lectnolsgy output shows trat the hypothesis tost has power of 0.4479 of aupeorthg the clain that p C7 houre of sleeg whee the actual populstion mean is 4.5 hours of sloep. Interprot this value

Answer 1

In a hypothesis test, a power value of 0.4479 suggests a moderate ability to detect a true difference in the population mean if it exists.

Step-by-step explanation:

The student is asking about the interpretation of a power value of 0.4479 in a hypothesis test. In a hypothesis test, the power represents the probability of correctly rejecting the null hypothesis when it is false.

In this case, the null hypothesis is that the mean amount of sleep for adults is equal to or greater than 7 hours, while the alternative hypothesis is that the mean amount of sleep is less than 7 hours.

The power of 0.4479 indicates that there is a 44.79% chance of correctly rejecting the null hypothesis and concluding that the population mean is less than 7 hours of sleep when it is actually 4.5 hours.

In other words, the test has a moderate ability to detect a true difference in the population mean if it exists.

Overall, a power of 0.4479 suggests that the hypothesis test may not be very sensitive to finding a significant difference, and there is a significant risk of a Type II error (failing to reject the null hypothesis when it is false).

Answer 2

In a hypothesis test, a power value of 0.4479 suggests a moderate ability to detect a true difference in the population mean if it exists.

Step-by-step explanation:

The student is asking about the interpretation of a power value of 0.4479 in a hypothesis test. In a hypothesis test, the power represents the probability of correctly rejecting the null hypothesis when it is false.

In this case, the null hypothesis is that the mean amount of sleep for adults is equal to or greater than 7 hours, while the alternative hypothesis is that the mean amount of sleep is less than 7 hours.

The power of 0.4479 indicates that there is a 44.79% chance of correctly rejecting the null hypothesis and concluding that the population mean is less than 7 hours of sleep when it is actually 4.5 hours.

In other words, the test has a moderate ability to detect a true difference in the population mean if it exists.

Overall, a power of 0.4479 suggests that the hypothesis test may not be very sensitive to finding a significant difference, and there is a significant risk of a Type II error (failing to reject the null hypothesis when it is false).