Question#1
1- In a certain population of fish, the lengths X of the individual fish follow a normal distribution with μ = 54 mm and standard deviation σ = 4.5 mm
Let x̄ be a mean length of a sample of 4 fish. What are mean and
standard deviation of the sampling distribution of x̄ for samples of
size 4 Round your answers with 2 decimal places.
μ x̄=σ x̄=
b)What
percentage of samples of 4 fish will have a mean length x̄ between 51
and 60 mm? Round your final answer to nearest tenth of a percent.
Question # 2
Confidence interval
Suppose a random sample of 4 fish, gave a sample mean length x̄=52.mm Assume that population standard deviation σ =4.5 mm is a correct value :
, Obtain 90 % confidence interval for mean x̄ Round final answer to 2 decimal places:
, what sample size is needed for 90 % CI for(mean) to have a margin of error of no more than 1.5 mmi?
Questio#3
Random sample of 30 female Sumatran elephants had mean shoulder height x̄ =216.2 cm with standard deviation s= 51.1 cm.
Do we have at 1 % significance level that mean shoulder height of female Sumatran elephants (μ) is over 2 meters (200 cm)?
Test appropriate hypotheses by means of a t-test.
a)Formulate null and alternative hypotheses, use proper notation,
b) Compute the appropriate test statistics
c)
Give the rejection region for your test, include appropriate sketeh.
marking critical value(s), and clearly label rejection and non-rejection
areas.
d) Compute a p-value for your test. Include appropriate
sketch explaining what you are computing. You may use a calculator or
estimate it from tables.
p-value=
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