Problem 17

  1. Propspective Study

  2. h0: p1-p2=0 ha: p1-p2 !=0

p1 = lenient p2 = strict

  1. Yes, 10%, random, indpendent of each other, samples within studies are independent

  2. p value = 0.24

This p value is too high to make a meaningful conclusion. The probablity that the results we saw were dut to random sampling variation are too high to reject the null

  1. There is a 24 % chance that the results we saw were due to random samling variation.

  2. Type II Error

Problem 19

  1. (-0.0649, 0.22125)

  2. We are 95% confident that the true difference between parents who are scrtic and those who are lenitent who have kids who smoke are between the values -0.0694 and 0.22125.

  3. 95% confident means that of all samples that extend their interval to the same amount of standard deviations we did will contain the true proportion.

Problem 21

  1. observational study

  2. h0: p1-p2=0 p1-p2 !=0

p1 = older p2 = younger

p value = ~0

we are 95% confident that the true difference of the values p1 and p2 is between the interval 0.099 and 0.277. It is most likely that there is a signifciant difference between the two groups, and we should reject the null hypothesis.

Problem 23

  1. h0: p1-p2=0 p1-p2>0

p1 = before sex p2 = after sex

630 people is less than 10% of all voters, and we assume voters were chose randomly. We also assume that the two groups are independent of each other.

340 / 630 515 / 1010

p value = 0.12

We cannot reject the null with a p value of 12%. The probabilty this variationw as due to random sampling variation is too high.

  1. type II

Problem 25

white: 94/3132 black: 20/606

h0: p1-p2=0 ha: p1-p1 !=0

p1=white people mult birhts p2=black people mult births

p value = 0.695

This value is way too high to dismiss the null. In fact, it’s more than probable that the results we saw were due to random sampling variation then there is any difference whatsoever in births

Type 2

Probelm 27

  1. (0.669, 0.83)

  2. (0.519, 0.703)

  3. Yes, they overlap. Maybe the medicines are actually the same effectiness

  4. (0.16, 0.26)

  5. No, this contains no zero. This means we are 95% confident that the true difference in effectiveness of these medications is above zero: meaning one is more effective than the other.

  6. Random variables are combined in part C, which skews the results. Part E is more correct sicne we use the pathagorem theomen of statistics and find the right standard deviation.