Question

Suppose that for the
past several decades, daily precipitation in Seattle, Washington
has had a mean of 2.4 mm and a standard deviation of 11.4 mm.
Researchers suspect that in recent years, the mean amount of daily
precipitation has changed, so they plan to obtain data for a random
sample of 195 days over the past five years and use this data to
conduct a one-sample *?*z‑test of
*?*0:*?*=2.4H0:μ=2.4 mm against
*?*1:*?*≠2.4H1:μ≠2.4 mm, where *?*μ is the
mean daily precipitation for the last five years. Although they
realize that rainfall does not follow a normal distribution, they
feel safe using a *?*z‑test because the sample size is
large.

The researchers want
to know what the power of this test is to reject the null
hypothesis at significance level *?*=0.05α=0.05 if the
actual mean daily precipitation is 2.6 mm or more. Computing power
by hand requires two steps.

The first step is to use a significance level of 0.05 to determine the values of the sample mean for which they will reject their null hypothesis. Give your answer to the nearest 0.1 mm.

The researchers will reject their null hypothesis if the sample mean is

less than_____mm or

greater than_____mm

In the second step, find the power of the test by first assuming that the the actual mean is 2.6 mm. Then, compute the probability of getting a sample mean in the rejection region found in the first step. Leave the boundaries of the critical region rounded to one decimal place in your calculation, and give your answer as a percentage rounded to two decimal places.

Power = ______%

Answer #1

Given the sample size = n = 195, population standard deviation = , to test the null hypothesis v/s the alternative hypothesis , at alpha = 0.05, the test statistic, reject H0 if , where, ,

therefore, for H0, , Therefore, , therefore, reject H0 if

, or

The actual mean = , therefore, power of the test =

P[Z>1.71] = 0.0436

Therefore, Power = 4.36%

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in the region and the recurrence interval of precipitation with
this value. ...... b.) The standard deviations of the maximum daily
precipitation observed at two neighboring meteorological stations,...

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H₀: μ ≤ 0
H₁: μ > 0
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considering which factors might decrease power so that you can
adjust your plans to avoid them, if possible, before conducting
your research.
The following are your considerations for decreasing power. Fill
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Suppose the hypothesis test
H0:μ=12H0:μ=12
against
Ha:μ<12Ha:μ<12
is to be conducted using a random sample of n=44n=44
observations with significance level set as
α=0.05α=0.05.
Assume that population actually has a normal distribution with
σ=6.σ=6.
Determine the probability of making a Type-II error (failing to
reject a false null hypothesis) given that the actual population
mean is μ=9μ=9.
P(Type-II error) ==

The recommended daily dietary allowance for zinc among males
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Does this data indicate that average daily zinc intake in the
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State the appropriate null and alternative hypotheses.
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Test the claim that the mean GPA of night students is larger
than 2.4 at the 0.025 significance level.
The null and alternative hypothesis would be:
H0:p≤0.6H0:p≤0.6
H1:p>0.6H1:p>0.6
H0:μ≤2.4H0:μ≤2.4
H1:μ>2.4H1:μ>2.4
H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
H0:p≥0.6H0:p≥0.6
H1:p<0.6H1:p<0.6
H0:μ≥2.4H0:μ≥2.4
H1:μ<2.4H1:μ<2.4
H0:μ=2.4H0:μ=2.4
H1:μ≠2.4H1:μ≠2.4
The test is:
two-tailed
right-tailed
left-tailed
Based on a sample of 75 people, the sample mean GPA was 2.43 with a
standard deviation of 0.05
The p-value is: (to 2 decimals)
Based on this we:
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Fail to reject the...

The mean lifetime for cardiac stents is 8.9 years. A medical
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manufacturing process and hypothesizes that the lifetime is now
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evidence of a prolonged lifetime of the stents?
Run a hypothesis test at α = 0.05 level of significance
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Step 1. Set up hypotheses and...

For the past several years, the mean number of people in a
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Test the claim about the population mean μ at the level of
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Write out null and alternative hypotheses, your critical z-score
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Claim: μ > 28; α = 0.05, σ = 1.2
Sample statistics: x̅ = 28.3, n = 50
H0:
Ha:
Critical z-score:
Z test statistic:
Decision:

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Solve in steps
The mean yearly salary for high school teachers in Texas is
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Step 1: Null Hypothesis and Alternative Hypothesis
Step 2: Value for...

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