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1. Surveys, Inc. completed a SRS of 50 ice cream parlors in Syracuse asking how long they have been in business. They found that x = 7.438 years. Also, suppose they know that σ = 10.12 based on results from similar cities in NY. Create a 90 percent confidence interval for the population mean based on this information. 

1. Suppose that Fizzy Pop claims that their diet cola contains exactly one calorie. Their quality control division wants to test the veracity of this claim, and they ask you to conduct a hypothesis test with α = 0.05. You randomly select 100 diet colas and measure the number of calories. You find that x =1.025 calories, and you know that σ = 0.10 calories. Complete the test. Show all work.

1. Given the value of x and σ in question 2, what is the smallest sample size that you could have drawn and reached the same conclusion? 

4) Suppose that you are testing the following hypothesis: H0: μ = 300 Ha: μ < 300 With a sample size of 6 (yes, I know it is too small, but let's assume it is not) and the population has a normal distribution with σ = 3.0. A 5% significance test rejects H0 of z ≤ -1.645, where the test statistic is 

z=x-300/3/√6

1. a) Find the power of this test against the alternative μ = 298. b) Find the power against the alternative that μ = 294. c) Is the power against μ = 296 higher or lower than the value you found in (b)? Explain why this result makes sense. 

5) Use the results from question 4 to give the probabilities of Type I and Type II errors for the test discussed there. Take the alternative hypothesis to be μ = 294.

(7y³+5y-1) + (2y² - 6y +3)

I'm looking for literally, step by step breakdown of this problemwith written descriptions of what you are doing, I know this issimple, but math is not my strong suit.

Thanks!

1.5 x 10^-6 = x^2/0.175

I know it's simple math but please provide a step by step breakdown please?
thanks!

Find the angle of an intersection between diagonals of a rectangle with sides 6 and 4 

What is the mean and variance if you roll the die n times?