Chapter 1. Tutorial: Thinking About Inference - Power

1.1 Problem Statement

{64.1, 64.2, 64.3, 64.4, 64.5, 64.6, 64.7, 64.8, 64.9}
rand(0,8)
@height[$heightindex]
{60, 65, 70, 75, 80, 85, 90, 95, 100}
rand(0,8)
@sample[$sampleindex]
{2, 2.5, 3, 3.5, 4}
rand(0,4)
@stddev[$stddev]
{.10, .05, .01}
{0,2}
@significance[$significanceindex]
$height-0.5

The power of an experiment to detect an effect depends on four attributes of the experiment:

  • Significance level
  • Size of the effect
  • Variation of value
  • The sample size

The average height of 22-year-old American women is $height inches. You wonder whether the mean height of this year’s female graduates from your local college is less than the national average because the local economy has been doing poorly which often leads to poorer nutrition. You measure a simple random sample of $sample graduates. The standard deviation of individual heights is $stddev inches. A difference of .5 inches in the mean would indicate a large effect of the poor nutrition. All tests will be done at the $significance level.

1.2 Step 1

questions

Question 1.1

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
Correct.
Incorrect.

Question 1.2

NIyDIR2MGwnx4l8x3UB8eZdaKAsSHHMweW+OvBBkqkuU9WD/sVswG1+yIn+eZr1pS6vl8K4Ualt617ER
Correct.
Incorrect.

Question 1.3

jz8yXpSC+9Rpggqqst8HOCfC173Q9Vwfj0S6D16ffYgjLhZfJwPNW+j5XA5YD8xu
Correct.
Incorrect.

Question 1.4

The hypothesized mean if there was no nutrition effect is ULd/zwxBJ9PMHKKX inches. The mean if there is a nutritional effect is qTMhdhYw8ZZJjDKxssVHtQ==.

Correct.
Incorrect.

1.3 Step 2

questions

Question 1.5

ocjSc6prMlov46JQXiufg4IP1krXvfJv1jJtdoVrnSNzSe2yUqwgSFZCgOaw+DutcdJ3FDWW/TUtxIPvaykSonj1V6o=
Correct.
Incorrect.

Question 1.6

If the significance level was reduced, the power would t+vsIRVE1c8B0BG+BkSmZshLzpCzuiGU+5PihANYzsm8q46+k4GpQQ==.

Correct.
Incorrect.

Question 1.7

If the size of the effect was increased, the power would m8EjxnmOgDg9zXUOFPbRgYrf0BP8P2b3toES4W4NmnYl9FZZ4PqBxA==.

Correct.
Incorrect.

Question 1.8

If the standard deviation of individual values increases, the power would t+vsIRVE1c8B0BG+BkSmZshLzpCzuiGU+5PihANYzsm8q46+k4GpQQ==.

Correct.
Incorrect.

Question 1.9

Finally, if the sample size were increased, the power would m8EjxnmOgDg9zXUOFPbRgYrf0BP8P2b3toES4W4NmnYl9FZZ4PqBxA==

Correct.
Incorrect.

1.4 Step 3

The following picture, which is just an example of the applet you will be working with, was taken from the Power applet

http://www.whfreeman. com/ips7e

questions

Question 1.10

EdNJKa5qkE4jEvMtNKko2iY9cUd4iWRlQyCwzk1Bacg4OXvpEyvwD+Sd/iFsUp3iXr/sIWMfeIpJ9w6ZTWopthyWxsEfWBADw6lJL/4b/nocRapA3JVlcE2o1Hjyz1wimAOVq6yrUyi6uDZHtcqmHJZWX5uTOlUSlJWFdrS2ImuBmU62F3ejjbqx+dROvy4fVnjdCR3yMoewuLSOWhNC8Pt81JnVe74GPHGZoJd/Cpvr2zQCB2t2jB+jBdgpFFJX1tKVHSPAi8T7HPtm3rdC35zZofmWXtlG7yFdpGAkrBnc3TwcFQh/wTghhZgBqrmaCH5wcFlnXvDCD+azwQ3PLEF3jJe6CePZvhBVgYIQTp7kaCpwJLL2VJM8uyG0zrWnPjig971I1B9gpFuQdeE+7slZZsV4+y6finVRWuvJbfzzPTuKX7vZSGXF7kdXnemEnD6ZRSGkqUqt4nVxtnyIgw==
Correct.
Incorrect.

Question 1.11

3/jQb/c3ADqAYF386MYoCBYqHlQwLWDuHEU7+UMjYQVpWc7GUNq85Ob9H14URJMwQVoOon8FpygcTT/YcQ5avml8qAzfBmToWNTaL/RvIStvGgxwQQxbuWMRZwucxQ4NaziTz8z1Vkr72EXeWEbbE5qMf3zcqu7mZVP61p/6Uyl0ccV/sgK5TUumEOP7bytgPQNlgl/30uvTaUVHSvCF64y8ENQ0SlJXIq9dWIcRlv0TQYOMG9kZX/7DkME+7+EEVsnnhuyyXdPm+sDNT52NS/FJSMHJDhv/ooW9hEG5R3vFYjmDtK8aOrYulxoFVEPuYABZ+w+Poz0xKwSCIXC0sHUMxxem1CYHca8MBbREbSXwqKYmJE/AaT7GOjD43TvswVo07F1bdUhbAQ9AdK1b0/fJXzbIP8X08dT9VXNypk8V+2VI8My27XHQphu02cOpBwzn3cSSMwHYfI625CDTFiEfa9M=
Correct.
Incorrect.

Question 1.12

9OjeDbjnnfvKcqzrfsv3wamh1xJkhZvbibNuAdVr/cr8JDDCrB0eESoYz4X4I8BW0gWqcc5lTgt463apBJHsTVqcPiXiC8JUF1VLBcBH2SKSGqE11uSN2hhjyUHglKS5WQKKoFYYEoy5LclhOAv4/X6Z9473TTEcwQkq7m8T+Q02zc1ByoLXScFOdsjt2i2+qb503rod6mmU+y5/xZmoQ9hwRduLJCjAW7dPvqhbNPeh9wIFb3yD9bQvnfNHaI5cR9QuW02eEpaxJ8NQMMtLQ583/mL7kJCteRpmJWs4Buh3dK09ASMNyTpRbt6Ku3MPZB03xqmESZM27mYio73z13Z1sf8KVdI2PpPSoUR7bOWgDSZVflZ9Oa461h+dD5N2fxDOjPBUsB9mjHyWq10NJ4ka72gLU7uHSzK4gVs6iLQH/dgGJX6PQseTGQ7598Nr
Correct.
Incorrect.

Question 1.13

iN8jkC03AYOk9otUwFtP11hrwfaHaPchzNRapOf2hpZ/p345YksvPanbG3bKL/dccKjoO/3h+bCaxa8uRc3fh94TnVSdPxVmIAbc3kUf+WDxcxO1/4pxlXurvtoVJtTNNYPsl3lJgbJ+Iq3QheSBUWPO79NRvRonDU59gqgpYDIuIqS29DAS48YKaqq3IYPvWbTU0W0gMwf5uQzwQNQ9CJ2vP654D+gqw6rfM/GZRXS+bWaLqLsStLvOV2pPKKm6fBjLT/lgK8JmD04JIEvJbaVZ0BtEqMxy1+L5l5lkumhxY9ToyTtFg4EisSRb+uL3lfyITGuWNyIK6kAPFrRNF6sMkpZHS6SJmqXzLaJWzgz4eGguHPelo8lmJn+RLhobsdCjmMWQYU9tr8bqifWesQRNBsAH5TWf3vzUbicrFhOy4v6oLi+NEseAq1Q8MIow5qqsKA==
Correct.
Incorrect.