## Drawing Inferences about Population Means and Porportions

Module 4 SLP – Drawing Inferences About Population Means and Proportions

BHS220 Introduction to Health Statistics

Trident University International

**1. ****Identify a test statistic to help you assess the evidence against the null hypothesis ****you**

**developed in the previous module.**

The test statistic I selected to help validate the evidence for or against my null hypothesis is a one sample T test.

**2. ****Explain why you have chosen the specific test statis****tic. Include in your discussion**

**description of the test statistic.**

I selected the one sample T test because a one sample T test will compare the mean of my exercise sample data to the population mean of sixty minutes that was presented in an article by Shanks (2010), in The Harvard Gazette. Additionally, I think the one sample T test is the appropriate statistical test to perform is because although I have the hypothetical mean of sixty minutes, I do not have the population standard deviation and I have a small sample size to work with (Stephanie, 2018).

**3. ****Summarize your findings by creating a summary graph in which you display your data.**

The data I collected recorded the amount of time I exercised daily for a one-week period.

Table 1. Daily exercise data.

DATE | MINUTES OF EXERCISE |

1 | 72 |

2 | 82 |

3 | 48 |

4 | 68 |

5 | 75 |

6 | 50 |

7 | 25 |

Table 2. Microsoft Excel summary statistics of the exercise data.

Mean | 60 |
---|---|

Standard Error | 7.537 |

Median | 68 |

Mode | #N/A |

Standard Deviation | 19.942 |

Sample Variance | 397.667 |

Kurtosis | 0.033 |

Skewness | -0.863 |

Range | 57 |

Minimum | 25 |

Maximum | 82 |

Sum | 420 |

Count | 7 |

Confidence Level(95.0%) | 18.443 |

Table 3. Results of the exercise data T testing.

Exercise Data T Test | Exercise Data |
---|---|

Mean | 60 |

Variance | 397.667 |

Observations | 7 |

Hypothesized Mean | 60 |

df | 6 |

t Stat | 0 |

P(T<=t) one-tail
| 0.5 |

t Critical one-tail | 1.943 |

P(T<=t) two-tail
| 1 |

t Critical two-tail | 2.447 |

Using Microsoft Excel to conduct a T test, Table 2 displays the results of the T test.

With a significance level of 0.05, the p values for both, one tail and two tail testing are greater than 0.05. Because the p values are greater than 0.05, the null hypothesis should not be rejected. The results of the T test indicate that the mean of my exercise data is not significantly different than the population mean of sixty minutes.

**4. ****Discuss the total number of measurements (sa****mple size), the possibility for**

**measurement error, and whether it is large enough to paint an accurate picture.**

The exercise data in Table 1 consists of a sample size of seven recorded events which is considered a small sample size. Because my sample size is small, statistical testing may produce inconclusive test result, larger sample sizes can help researchers detect smaller effect sizes (Fitzpatrick, 2015). Larger sample sizes help reduce the potential for Type II errors which can occur when testing results actually confirm they hypothesis when in actuality, the alternative hypothesis is true. Sample sizes that are too small tend to increase the possibility of presenting Type II errors into the testing process, which could skew the testing results (Deziel, 2018)**. **

Regarding my exercise data, it is not large enough to paint an accurate picture since it only represents one week’s worth of data. Ideally, I think at a minimum, thirty days’ worth of data should be collected to help paint a more realistic picture of my exercise activities.

References

Deziel, C. (2018). The effects of a small sample size limitation. Retrieved from https://sciencing.com/effects-small-sample-size-limitation-8545371.html

Fitzpatrick, R. (2015). Why is sample size important? Retrieved from https://blog.statsols.com/why-is-sample-size-important/

Shanks, L. (2010). 60 minutes of exercise per day needed for middle-aged women to maintain weight. *Harvard Gazette*. Retrieved from https://news.harvard.edu/gazette/story/ 2010/03/60-minutes-of-exercise-per-day-needed-for-middle-aged-women-to-maintain-weight/

Stephanie. (2018). One sample t test: how to run it, step by step. Retrieved from http://www.statisticshowto.com/one-sample-t-test/

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