4.4 Heights of adults

a-) Height mean 171.1 Height median 170.3

b-) Standar Deviation:9.4
IQR = 177.8 - 163.8 = 14

c-) the student of 180 cm is in the one SD which is not considered unusual even that is above the average and the 155 is 2 SD away and also no consider unusual.

d-)no. because of the variation of the new sample size. it can be close range but not the same.

e-)9.4 / sqr(507) = 0.417

4.14 Thanksgiving spending, Part I

a-) False, the interence shoudl be measure on the population not in a sample or point estimate.

b-) False, we have a pretty good sample size even the that is skewed.

c-)False, any random sample can any different range.

d-)True, average.

e-)True, will be smaller range interval and this will be more narrow.

f-)False, we need to 3^2, 9 more times

g-) True, (89.11−80.312)/2 =4.4

4.24 Gifted children, Part I

a-) Yes, we have a random size over 30.

c-)Interpret the p-value in context of the hypothesis test and the data.
P: 0.0256503 we fail to reject H0

d-) (30.69 ± 1.65) ∗ (30.69 ± 1.188) =(29.50,31.88)

e-)Yes, the result obtained fall outside of the interval values.

4.26 Gifted children, Part II.

a-) (118.2 - 100) / (6.5/6) = 16.85 reject the null hypothesis H0 we select the H1 “the mother’s IQ is different from the population”

b-) confidence interval(116.4179 - 119.9820)

c-)Do your results from the hypothesis test and the confidence interval agree? Yes,90 % confidence IQ is between 116.42 and 119.98 above the population mean.

4.34 CLT

Define the term “sampling distribution” of the mean, and describe how the shape, center, and spread of the sampling distribution of the mean change as sample size increases.

The sample distribution of the mean shows the graph shape of random selected observations and we can see that increasing values we will have a smaller SD and also a more close sample mean to the whole population.

4.40 CFLBs

a-) 0.0668

b-)1000/sqrt(15) = 258.1989

c-)(10,500 - 900) / 258.1989 = 5.809 = p-pnorm = it will be close to zero.

d-)

library(ggplot2)
library(dplyr)
## Warning: package 'dplyr' was built under R version 3.5.2
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
mean_val <- 9000
n_val <- 100000



samp1 <- rnorm(n_val, mean = mean_val, sd = 1000)
samp2 <- rnorm(n_val, mean = mean_val, sd = 258.1989)
df <- data.frame(samp1 = samp1, samp2 = samp2)

df %>% ggplot() + geom_density(aes(x = samp1)) + geom_density(aes(x = samp2))

4.48 Same observation, different sample size

as our value will be increasing from 50 to 500 our p value and Stadard Deviation should be decreasing.