Statistics tasks

An analytician is studying the profits of a company over the course of ten years. Let X be the number of years after the inital year the analytician is studying. Y is the profits in year X and the analytician believes the profits are a normal distribution stochastic(random) variable with expectation ?(?)=?0+?1? and standard deviation ?=0.08. Based on these observations the analytician finds that:
?¯=3.6 and ?¯=4.26
?=?^9_?=0 (????¯)^2=7.44,
?^9_?=0 (????¯)??=4.96

(I added this as a picture too as I have a hard time writing formulas on here)

Questions:

1. Estimate ?0 og ?1.

2. Can it be proven that the yearly increase in profits, ?1, is bigger than 0.5? Formulate fitting hypothesis and do a hypothesis test at 0,5% significance level.
Critical value=
H1 or not H1?

3.Find a 99% confidence interval for expected profits for x=5
Upper confidence limit:
Lower confidence limit:

4. Find a 95% prediction interval for expected profits for x=1
Upper prediction limit:
Lower prediction limit:

Answer

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