Question

6. (8 points) One histogram shows the distribution of ages of 300 pennies. The other two graphs show distributions of means from random samples taken from the same population of pennies. One histogram shows means based on samples of 5 pennies, and another shows means based on samples of 100 pennies. Each graph with means was done with many repetitions. Which distribution is which, and how do you know? Aeuency 20 IS AGE AGE C F.equency Population: Sample size 5: Sample size 100: Explain your choices: 20 25S 15 AGE 10 6. A random sample of 13 women's resting pulse rates from the National Health and Nutrition Examination Survey (NHANES) showed a mean of 73.5 beats per minute and standard deviation of 17.1. Assume that the pulse rates are Normally distributed. (a) 2 points) What value should be used for t" (Use the t-table in the appendix of your texthook) (b) (4 points) By hand, find a 95% confidence interval for the po steps involved. pulation pulse rate of women. Show the

Answer 1

5. Population data graph shows right skewness as the heights of bars are higher at lower relatively to the higher values.

Sample of 5 data graph shows left skewness as the heights of bars are lower at lower relatively to the higher values.

Sample of 100 data shows symmetric data as the tails are fairly equally spread and bars first rise and then fall showing symmetricity in the data.

6. t value that should be used is-

= t_13-1,0.025

= t_{12, 0.025}

= 2.179

95% confidence interval will be calculated as-

$\dpi{100} \overline{X}\pm t_{12,.025}*\frac{s}{\sqrt{n}}$

where $\overline{X}$ = 73.5 and n = 13 and s (sample standard deviation) = 17.1

Thus required confidence interval is

( 63.167 , 83.833 )

Answers

TY!