Question

C:/Users/norma/Desktop/STAT255/stat255supplement2020.pdf A) 朗读此页内容ys 99 14 EXTRA PROBLEMS 5. Normally the leaves of the Mimosa pudica are horizontal. However, if one of them is touched lightly, the leaflets will fold. It is reported that , the true mean time from touch to complete closure is 3.0s. An experiment is run to test this value. A random sample of size observations on the elapsed time (seconds) from touch to complete closure yields the following data: 3.2, 4.4, 3.5, 2.9, 4.2, 2.8. Assume the population distribution of elapsed times is normal. (a) Compute a 90% confidence interval for u. (b) Use the results of the sample as a pilot study to determine the sample size needed to estimate ji within £0.20s with 95% confidence. (c) Use the results of the sample as a pilot study to determine the sample size needed to within 20.30s with 95% confidence. I estimate 14.19 Set 22 Confidence intervals for population proportions 1. A random sample of 487 non-smoking women who had given birth was selected. 7.2% of these births resulted in children of low birth weight (< 2500g).

Can you the answer with formula plz

and I can not find Z0.05 in the table

Answer 1

(a) x = 3.5

s = 0.669

n = 6

df = 6 - 1 = 5

The t-critical value for df = 5 and $\alpha /2 = 0.05$ from the t-table is 2.015.

The 90% confidence interval will be:

= x ± t*(s/√n)

= 3.5 ± 2.015*(0.669/√6)

= (2.9494, 4.0506)

(b) E = 0.20

z = 1.96

s = σ = 0.669

n = (1.96*0.669/0.20)^2 = 44

(c) E = 0.30

z = 1.96

s = σ = 0.669

n = (1.96*0.669/0.30)^2 = 20