Question

Using the mean and standard deviation you found in question 2​ (to all four decimal​ places), find and interpert a​ 99% confidence interval for the mean height of all​ 5-year-old females.

1. Confidence interval​ (round to one decimal​ place)   

2. Interpret the confidence interval in the SHOW YOUR WORK area.

3. You find that a classroom of 30​ five-year-old females have a height of 43.8 inches. Based on your​ findings, you can conclude​ that:

A. the classroom of 30 is shorter than average since 43.8 inches is below the interval found.

B. the classroom of 30 is average since 43.8 inches is within the interval found.

C. we cannot make any conclusions...statistics is not a science after all.

D. the classroom of 30 is taller than average since 43.8 inches is above the interval found.

E. the classroom of 30 is taller than average since 43.8 inches is above the mean found.

Question 2:

44.5	42.4	42.2	46.2	45.7	44.8	43.3	39.5	45.4	43.0
43.4	44.7	38.6	41.6	50.2	46.9	39.6	44.7	36.5	42.7
40.6	47.5	48.4	37.5	45.5	43.3	41.2	40.5	44.4	42.6
42.0	40.3	42.0	42.2	38.5	43.6	40.6	45.0	40.7	36.3
44.5	37.6	42.2	40.3	48.5	41.6	41.7	38.9	39.5	43.6
41.3	38.8	41.9	40.3	42.1	41.9	42.3	44.6	40.5	37.4
44.5	40.7	38.2	42.6	44.0	35.9	43.7	48.1	38.7	46.0
43.4	44.6	37.7	34.6	42.4	42.7	47.0	42.8	39.9	42.3

Find the following descriptive statistics using StatCrunch. Insert the StatCrunch output in SHOW YOUR WORK.

What is the​ mean? (Round to 4 decimal​ places)

x =42.2238

s​ = 3.131

Answer 1

1) .The formula for CONFIDENCE INTERVAL estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 42.2238
Z = 2.58 CALCULATED FROM Z TABLE SHOWN BELOW AT 99% CONFIDENCE LEVEL
s_M = √(3.131²/80) = 0.35

μ = M ± Z(s_M)
μ = 42.2238 ± 2.58*0.35
μ = 42.2238 ± 0.901686

99% CI [41.3, 43.1].

2) Interpretation: .

we can be 99% confident that the population mean (μ) falls between 41.3 and 43.1.

3) For the given value of average for 30 stdents of a class room the conclusion would be

D. the classroom of 30 is taller than average since 43.8 inches is above the interval found.