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 andstandard deviation of the sampling distribution of x̄ for samples ofsize 4 Round your answers with 2 decimal places.

μ x̄=σ x̄=

b)Whatpercentage of samples of 4 fish will have a mean length x̄ between 51and 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-rejectionareas.

d) Compute a p-value for your test. Include appropriatesketch explaining what you are computing. You may use a calculator orestimate it from tables.

p-value=