# problem 8

**STAT 200 Week 5 Homework Problems**

**7.1.4**

Stephen Stigler determined in 1977 that the speed of light is 299,710.5 km/sec. In 1882, Albert Michelson had collected measurements on the speed of light (“Student t-distribution,” 2013). Is there evidence to show that Michelson’s data is different from Stigler’s value of the speed of light? State the random variable, population parameter, and hypotheses.

**7.1.6**

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (“Consumer fraud and,” 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.

**7.2.4**

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (“Consumer fraud and,” 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? Test at the 5% level.

**7.2.6**

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) (“Autism and developmental,” 2008). Nationally 1 in 88 children are diagnosed with ASD (“CDC features -,” 2013). Is there sufficient data to show that the incident of ASD is more in Arizona than nationally? Test at the 1% level.

**7.3.6**

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #7.3.8 (“SOCR data 2008,” 2013). Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

**Table #7.3.8: Economic Dynamism of Middle Income Countries**

25.8057 | 37.4511 | 51.915 | 43.6952 | 47.8506 | 43.7178 | 58.0767 |

41.1648 | 38.0793 | 37.7251 | 39.6553 | 42.0265 | 48.6159 | 43.8555 |

49.1361 | 61.9281 | 41.9543 | 44.9346 | 46.0521 | 48.3652 | 43.6252 |

50.9866 | 59.1724 | 39.6282 | 33.6074 | 21.6643 |

**7.3.8**

Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 (“Maintaining balance while,” 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.

**Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects**

19 | 30 | 20 | 19 | 29 | 25 | 21 | 24 | 50 |

**8.1.4**

Suppose you compute a confidence interval with a sample size of 100. What will happen to the confidence interval if the sample size decreases to 80?

**8.1.8**

In 2013, Gallup conducted a poll and found a 95% confidence interval of the proportion of Americans who believe it is the government’s responsibility for health care. Give the statistical interpretation.

**8.2.6**

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) (“Autism and developmental,” 2008). Find the proportion of ASD in Arizona with a confidence level of 99%.

**8.3.6**

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 (“SOCR data 2008,” 2013). Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.

**Table #8.3.9: Economic Dynamism ($) of Middle Income Countries**

25.8057 | 37.4511 | 51.915 | 43.6952 | 47.8506 | 43.7178 | 58.0767 |

41.1648 | 38.0793 | 37.7251 | 39.6553 | 42.0265 | 48.6159 | 43.8555 |

49.1361 | 61.9281 | 41.9543 | 44.9346 | 46.0521 | 48.3652 | 43.6252 |

50.9866 | 59.1724 | 39.6282 | 33.6074 | 21.6643 |

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