Question

Indoor natatoriums or swimming pools are noted for their poor acustic properties. The goal is to design a pool such that the average time that it takes low-frequencies sound to die is at most 1.3 seconds with standard deviation of at most .6 second. Computer simulations of a preliminary design are conducted to see whether these standards are exceeded. These data are obtained on the time required for a low- frequency sound to die:

Data:

1.8, 3.7, 5.0, 5.3, 6.1, 0.5, 2.8, 5.6, 5.9, 2.7, 3.8, 5.9, 4.6, 0.3, 2.5, 1.3, 4.4, 4.6, 5.3, 4.3, 3.9, 2.1, 2.3, 7.1, 6.6, 7.9, 3.6, 2.7, 3.3, 3.3

a. Show with a plot whether the normality assumption for the data is reasonable.

b. Design a test to verify whether standards for the average time μ are exceeded. Set the significance level to α = 0.05.

c. Are you going to reject the null hypothesis? Explain.

d. Find a 95% confidence interval for σ2.

Answer 1

CTiven Dato. Nocs to find themean armd sample sta»land deviation 0 x 3.9: M-i (27-3.97), (3.3-3.97),+ 3.3-3.9ר(2 Un

ト89 5.4712 (リNow-states the Null and aitennatívelfothes -statıs S.E(R)

3-11-3 365 і 0.345i - l.l36 26-05 aiR e Mull hyfothesis Ho

45 2 0-05 n 0 09s, 30 2. 0 5 2. 2 od2 l45.12 ^1)(3.52i 21 (3.512i 45-72 2 2 o.915/ 2'9 lis-722 The 95% Confidence interval fe?-- /2.2G) 6-4555)
Note:Due to little confussion about a bit so i couldn't solved if you want to answer for a bit please post it separately

Thank you.