• Class Acticity 17 starts here

This first part is copied from Class Activity 16, finish whatever you didnโ€™t get to:

Sleep deprived transportation workers. The National Sleep Foundation conducted a survey on the sleep habits of randomly sampled transportation workers and a control sample of non-transportation workers. The results of the survey are shown below.

hrs of sleep Control Pilots
<6 35 19
6-8 193 132
>8 64 51
Total 292 202
  1. If we want to test for statistically significant evidence of a difference between the proportions of truck drivers and non-transportation workers who get less than 6 hours of sleep per day what should our hypotheses be.

$H_0 : $

$H_A : $

  1. Will your model for the sampling distribution be the normal distribution or the t-distribution and why?

  2. Draw a picture of the sampling distribution. (you donโ€™t need to include the picture here, just make sure to draw one)

  3. At the 5% significance level, is there statistically significant evidence of a difference?

  4. Compare this to a 95% confidence interval for the difference in proportions (we have never done an example quite like this one before).

Class Acticity 17 starts here

  1. The local electric company says that customers pay less than $200 per month on average. A local reporter is suspicious of these claims and thinks that customers are spending more than $200 per month. A random sample of 35 customers bills during a given month is taken with a mean of 220 and a standard deviation of 45. Create a hypothesis test from the perspective of the reporter to test the claims of the company under a 5% significance level.

  2. Compute the power of the hypothesis test at detecting a mean of $220. (Make sure to draw a picture)

  3. A population of people has incomes with a standard deviation of ฯƒ=$9000. A random sample of 25 people had a mean income of $54,800. Perform a hypothesis test using a significance level of .05 to see if this data provides statistically significant evidence that the mean salary is different than $60,000.

  4. What is the power of the test at detecting a mean income of $ $ 57000$?