# Homework Assignment 9

**Due in week 10 and worth 30 points**

Suppose that there are two (2) candidates (i.e., Jones and Johns) in the upcoming presidential election. Sara notes that she has discussed the presidential election candidates with 15 friends, and 10 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 50% of votes.

Answer the following questions in the space provided below:

- Based on what you now know about statistical inference, is Sara’s conclusion a logical conclusion? Why or why not?

I think that Sara’s conclusion is not logical because she based it on the view of close friends who are not a true representation of the entire population. For statistical inference to be logic, it is necessary to have a large sample size and obtained from different regions to provide varied views about the presidential election. Statistical inference is a process that involves deducing properties based on an underlying distribution by data analysis. Thus, the sample size ought to be a true representation of the population to make a logical inference. Sara depended on the views of15 close friends who are likely to have similar political views.

Based on the poll, 19 people voted for candidate Jones: *p* = 19/27 = 0.7037 or 70.37%

And 8 people didn’t vote for candidate Jones: *q* = 8/27 = 0.2963 or 29.63%

n*p* = 15(0.67) = 10 > 5

n*q*= 15 (0.33) = 5 > 5

Null hypothesis H_{0}: P <= 0.5

Alternative hypothesis: H_{1}: P > 0.5

α = 0.05 (95% confidence interval)

We can use z test and our z statistic is:

= 1.37

The z statistic (1.18) is in the ** pink area**so we do not have enough evidence to reject the null hypothesis.

z |

0 |

-1.96 |

0.025 |

1.96 |

0.025 |

Blue region is the reject area of null hypothesis. |

- How many friend samples Sara should have in order to draw the conclusion with 95% confidence interval? Why?

31

And calculating the z stat. based on new sample size:

= 1.96 1.96 is in the ** blue area **or the rejection area.

Since 1.95 is in the rejection area, Sara has enough evidence to reject the null and support the alternative hypothesis that candidate Jones will get more than 50% of the votes and win the election. Sara will need to poll a larger group of people in order to get 95 % confidence that Jones will win.

The minimum sample size required by Sara to draw a conclusion with 95% confidence that Jones will win the election is 31. From the assumption that the margin of error is less than 0.17 (from the calculation that 0.67 – 0.5=0.17) and using the Z score which is 1.96; the minimum value of the sample can be obtained by the formula, n = p (1 – p) (Z / ME) ^2. Thus, for Sara to obtain the confidence level she desires, she ought to increase the number of people in the survey to a minimum of 31. A high number of participants in a survey results to a better inference to a logical conclusion of the presidential poll results.

- How would you explain your conclusion to Sara without using any statistical jargon? Why?

According to the calculations, Sara should not make a positive inference that Jones will win the presidential elections because she based her arguments on a small sample size that comprises of her close friends. The views of people keep on changing from one region to another depending on their preferences. Thus, Sara should not base her logical conclusion on a biased group of people likely to have similar political view. She requires conducting a comprehensive survey in different areas and having a large sample size to base her logic conclusion.In every population, there are diverse views about a poll, and hence a researcher ought to select a sample size which is a true representation of the population before making a statistical inference.