# Question: q2 hypothesis testing with a z test 14 points total...

###### Question details

**Q2. Hypothesis Testing with a Z test (14 points
total)**

A research institute examined the number of smart phones and
tablets connected to the internet in American households and
reported a mean (*μ*) of 5 devices per household and a
standard deviation (*σ*) of 1.5 devices. But I wonder if the
statistics in my neighborhood, Chandler, would be different from
the national average. To test this idea, I randomly picked 16
friends of mine living in Chandler and asked them how many smart
phones and tablets with internet access are in their households.
The data set is shown below.

I would like to perform a Z test to see if the number of mobile
devices in Chandler households (represented by the sample of 16
households) are significantly different from the number of devices
in the national households. The significance level for my Z test
was set at *α* = .05. The hypotheses should be
nondirectional because I am not predicting any specific direction
of difference, and the test should be two-tailed.

Subject # (Household) |
# of mobile devices |

1 |
5 |

2 |
7 |

3 |
6 |

4 |
5 |

5 |
5 |

6 |
7 |

7 |
5 |

8 |
8 |

9 |
4 |

10 |
4 |

11 |
3 |

12 |
6 |

13 |
5 |

14 |
4 |

15 |
4 |

16 |
6 |

a. What is the dependent variable in this study? (1 point)

b. What should be my null and alternative hypotheses? State each hypothesis using both words and statistical symbol notation. (2 points total. 1 for each hypothesis: .5 for written, .5 for notation)

*Note: The hypotheses should be non-directional.*

c. Calculate the sample mean. (1 point total: .5 if the process is correct but the result was calculated incorrectly)

d. Calculate standard error using the population standard
deviation σ given in the research scenario (*SE*, which is
the standard deviation of the sampling distribution) (2 point
total: 1 if the process is correct but the result was calculated
incorrectly)

e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) (2 point total: 1 if the process is correct but the result was calculated incorrectly)

f. Determine the critical Z value(s). Explain how you find the answer. (1 point: .5 for the Z value, .5 for the rationale)

g. Compare the Z statistic with the appropriate critical Z value (is the Z statistic more extreme than the critical Z?), and then draw a conclusion about the result of the hypothesis test (do you “reject” or “fail to reject” the null hypothesis?) (2 points: 1 for Z statistic comparison; 1 for hypothesis test decision)

h. Write 1-2 sentences to answer the research question (you can use the wording from the hypotheses or explain it in another way) (1 point)

i. Calculate the standardized effect size (2 point total: 1 if the process is correct but the result was calculated incorrectly)