Question

(a) <leave blank> (a) State the hypotheses; indicate which is the claim. (b) Verify that the conditions hold. (b) Verify that the conditions hold. (c) State the required standard score(s) (z, t, or x2). (c) Calculate the test statistic.* (Answer should be numeric value(s).) (d) Fully set up the confidence interval, without simplifying. * (d) Calculate the P-value. <leave the field blank> (e) Simplify and state your final confidence (e) Make the statistical conclusion. interval. (f) Interpret in context, in words. (f) Interpret in the context of the claim, in words. *For full credit, you must show work on paper for the test statistic and for confidence intervals (for both, fully set up the formulas before solving).

Answer 1

Please note we have followed the format given for confidence interval not hypothesis testing as question asks to calculate confidence interval.

a)

b)

In this case, the population is normally distributed so we can calculate the confidence interval.

c)

In this case, Chi square X² distribution will be used to calculate the confidence interval.

d)

Confidence Interval Formula for o is as follows: Square Root((n - 1)s?ix?12) <o<Square Root((n - 1)s21x21 - 012) where: (n-1) = Degrees of Freedom, s2 = sample variance and a = 1 - Confidence Percentage First find degrees of freedom: Degrees of Freedom = n - 1 Degrees of Freedom = 8 - 1 Degrees of Freedom = 7 Calculate a: a = 1 - confidence% a = 1 -0.9 a = 0.1 Find low end confidence interval value: Clow end = a/2 Clow end = 0.12 dlow end = 0.05

Find low end x value for 0.05 x?0.05 = 14.0671 <--- Value can be found on Excel using =CHIINV(0.05,7 Calculate low end confidence interval total: Low End = Square Root((n - 1)s-/xo/2) Low End = v(7)(14.6689y/14.0671) Low End = 102.6823/14.0671 Low End = 17.2994647084332 Low End = 2.7018 Find high end confidence interval value: A high end = 1 -a/2 Ahigh end = 1 - 0.1/2 Chigh end = 0.95 Find high end x= value for 0.95 x 20.95 = 2.1673 <--- Value can be found on Excel using =CHIINV(0.95,7) Calculate high end confidence interval total: High End = Square Root((n - 1982/X?1-02) High End = N(7)(14.6689y/2.1673) High End = V102.6823/2.1673 High End = 147.377981820699 High End = 6.8832

e)

2.7018 <<6.8832<---- This is our 90% confidence interval

f)

We are 90% confident that σ lies between 2.7018 and 6.8832. If we repeated the experiments, the proportion of such intervals that contains σ is 90%.