Question

Asked Apr 23, 2019

37 views

11.13 Attached. Thank you for answering my question!

Step 1

**The hypothesis:**

The hypothesis of interest is: *H*_{0}: *μ* = 0 vs. *H _{A}*:

The sample size is *n* = 25. The random sample is: *X*_{1}, *X*_{2}, …, *X*_{25}.

Step 2

**Power for normality assumption:**

Under the assumption of normal theory, *X*_{1}, *X*_{2}, …, *X*_{25} is from a normal distribution with parameters: mean 0.3 and standard deviation 1. The known standard deviation, *σ* is 1.

Thus, the sample mean for the sample of size 25 will have a normal distribution with mean 0.3 and standard deviation 1/√25 = 1/5 = 0.2.

The power of the test is the probability that the sample mean exceeds the critical value, that is, lies in the rejection region, when the alternative hypothesis, *H _{A}* is true. Using the given information, the value of

Now, *z _{α}*

The critical value for the test using sample mean is: *C* = *μ*_{0} + *z _{α}* ∙

Thus, the power of the test is calculated as follows:

Step 3

**Power for sign test:**

The normal distribution being symmetric, mean = median. So, here, median is *μ*.

For the sign test, denote *S* as the count or the number of observations among *X*1, *X*2, …, *X*25, that are greater than the hypothesized median,* μ* = 0.

It is known that half of all observations lie above the median and half lie below the median. If the null hypothesis, *H*0 is true, then the probability that an observation is greater than the hypothesized value 0 is 1/2 = 0.5. Here, sample size, *n* = 25.

Thus, according to the rules of a binomial model, *S* must follow the binomial distribution with parameters: number of trials 25 and probability of success...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: The government of a large city needs to determine whether the city's residents will support the bui...

A: Solution:Reasons for incorrect options:Opinions of other city residents who do not have children in ...

Q: what is the class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.

A: Class boundaries are those numbers which are used to separate the classes.It is the midpoint of the ...

Q: Find the standard deviation, s, of sample data summarized in the frequency distribution table given ...

A: Using the provided formula, the sample standard deviation of the provided frequency distribution is ...

Q: The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, ...

A: It is given that the match boxes are supposed to have an average of 40 matches per box with σ = 7. A...

Q: The number of unhealthy days based on the AQI ( Air Quality Index) for a random sample of metropolit...

A: Confidence interval:The (1-α) % confidence interval for population mean µ, when σ is unknown is give...

Q: Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advan...

A: The provided information are:

Q: Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adu...

A: The provided information are:

Q: A marketing manager for a cell phone company claims that more than 55% of children aged 8-12 have ce...

A: Null and alternative hypotheses:Here, to check whether more than 55% of children aged 8-12 have cell...

Q: The point on a normal distribution (mean equals 6 and standard deviation equals 9) that is greater t...

A: The given information is that the scores distributed normally with mean 6 and standard deviation 9.F...