6. (This is also the Sweetening cola example in topic 8): calculating power. The

Question

6. (This is also the Sweetening cola example in topic 8): calculating power. The cola maker of Example 15.7 wants to test at the 5% significance level the following hypotheses: H0: = 0 versus Ha: > 0 Ten taste scores were used for the significance test. The distribution of taste scores is assumed to be roughly Normal with standard deviation = 1. We want to calculate the power of this test when the true mean sweetness loss is = 0.8. (a) What values of the z statistic would lead us to reject H0? To what values of do they correspond? Use the inverse Normal calculations to figure this out.

When the true mean sweetness loss is = 0.8, how often would we reject H0? That is, what is the probability of obtaining sample averages like the ones defined in (a) when = 0.8? Use the z table to calculate this probability. This probability is the power of your test against the alternative = 0.8, the probability of rejecting H0 when the alternative = 0.8 is true.

If the sample size is increased to 20, compute the power.

If the significant level is decreased to 1%, compute the power.

Explanation / Answer

ans=

z= xbar – mu/ sigma (sqrt. n)

z= 1.645

Reject when xbar> 1.32

2. When the true mean sweetness loss is = 0.8, how often would we reject H0? That is, what is the probability of obtaining sample averages like the ones defined in (a) when = 0.8? Use the z table to calculate this probability. This probability is the power of your test against the alternative = 0.8, the probability of rejecting H0 when the alternative = 0.8 is true

Power= 0.9664

a.If the sample size is increased to 20, compute the power.

Z=1.65

Power= 0.9505

b.If the significant level is decreased to 1%, compute the power.

Z=2.34

Power= 0.9904

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