What is the probability researchers will reject their null hypothesis
MATLAB: An Introduction with Applications
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![estion 2 of 20
Attempt 14
Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample
50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the
supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one
month, o, is 1.5 lb.
To show that the supplement is effective, they plan to use a one-sample z-test of Ho: u = 0 lb against H:µ> 0 lb, where
is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01,
the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb.
What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or
more? Give your answer as a percentage, precise to two decimal places.
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Transcribed Image Text:estion 2 of 20
Attempt 14
Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample
50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the
supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one
month, o, is 1.5 lb.
To show that the supplement is effective, they plan to use a one-sample z-test of Ho: u = 0 lb against H:µ> 0 lb, where
is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01,
the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb.
What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or
more? Give your answer as a percentage, precise to two decimal places.
LEGO
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help
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Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
From the available information,
Population mean, = 0.7
Population Standard deviation, = 1.5
Sample size, n= 50
The standard error is,
Se ==0.2121
The level of significance is, = 0.01
From standard normal table at 0.01 level of significance the right tailed critical value is,
= = +2.326
The power of the test is denoted by .
Here is the probability of making type 2 error.
That is fail to reject the null hypothesis .
Reject Ho if
That is,
=
= 0+ * Se
= 2.326* (0.2121)
= 0.4933446
= 0.4934
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