2 & 3 STA308OHW 6.pdf X Solutions Recitation 6.pdf + V saka, unedu/access/conten

Question

2 & 3

STA308OHW 6.pdf X Solutions Recitation 6.pdf + V saka, unedu/access/content/group/702e45af-e2f8 43ca-a53c-9f1370003efaM0%20a0%20Recitations H 6 20 6pdf 2. In 1905 R Pearl published the article Biometrical Studies on Man. I. Variation and Correlation in Brain Weight". According to the study, brain weights of Swedish men are normally distributed with a mean of 1.4 kg and a standard deviation of 0.11 kg. Determine the sampling distribution of the sample mean for samples of size 3 a. b. Repeat part (a) for samples of size 12 That is, for parts (a) and (b) discuss the distribution, mean and standard deviation of the sample means for the different sample sizes. Use Excel to construct graphs similar to those shown in Fig 7.4 on page 321 in the textbook. Hand in your excel output and show the data you used to construct the plots, as well as the plots (see instructions below). No excel, no credit. c. d. Do you need to assume that brain weights of Swedish men are normally distributed to answer parts (a) and (b)? Explain your answer 3. Refer to question (2) in this assignment brain weights within 0.1 kg of the population mean brain weight of 1.40 kg. That is, Determine the percentage of all samples of three Swedish men that have mean between 1.3 and 1.5 kgs. Repeat part (a) for samples of size 12 a b. to search

Explanation / Answer

Solution2a:

sample mean=population mean=1.4

sample sd=population std dev/sqrt(n)

=0.11./sqrt(3)

= 0.06350853

Solutionb:

for n=12

sample mean=1.4

sample sd=std dev/sqrt(n)

=0.11/sqrt(12)

=0.03175426

we observe that as sample size increases std devaition (stanadard error of sample mean )decreases.

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