# 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

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

- answered
- 132 views
- $5.41

### Related Questions

- Statistics- Probability, Hypotheses , Standard Error
- Please check if my answers are correct - statistic, probability
- What is the normal probability distribution function?
- Statistical significance
- Probabilities
- Markov Chain
- Density plot
- Probability maximum value of samples from different distributions