# Question: a psychologist examined the number of electronic devices used for...

###### Question details

A psychologist examined the number of electronic devices used
for communication (computers, tablets, and smartphones) in the home
and reported a mean (*μ*) of 3.2 devices and standard
deviation (*σ*) of 1.8 devices. But I wonder if my circle of
friends has a different mean of devices in the home. To test this
idea, I randomly picked 16 friends of mine and asked them how many
electronic communication devices they have in their home. I would
like to perform a Z test to see if the number of devices in the
home among my friends is significantly different than the national
average. The significance level for my Z test was set at
*α*= .05.

Subject # |
# of devices |

1 |
2 |

2 |
3 |

3 |
4 |

4 |
3 |

5 |
5 |

6 |
3 |

7 |
4 |

8 |
3 |

9 |
2 |

10 |
2 |

11 |
4 |

12 |
4 |

13 |
3 |

14 |
5 |

15 |
4 |

16 |
7 |

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

- What should be my null and alternative hypotheses? State each hypothesis using both words and statistical notation.

*Hint: I am interested in any
difference from the national average so the hypotheses would be
non-directional.*(4 points total. 2 for the 2 notations, 2 for
the 2 written hypotheses)

- Calculate the sample mean. (2 points total, 1 for process/work, 1 for result)

- Calculate standard error (
*SE*, which is the standard deviation of the sampling distribution) (2 points total, 1 for process/work, 1 for result)

- Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) (2 points total, 1 for process/work, 1 for result)

- Specify whether the hypothesis test should be a two-tailed or a one-tailed test, and explain the rationale for the choice. (2 points total: 1 for chosen test, 1 for rationale)

- Determine the critical value for Z(1 point)

- Compare obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly state “reject” or “fail to reject” the null hypothesis (2 points: 1 for comparing the correct numbers and saying which one is more “extreme”; 1 for making the decision about null hypothesis.)

- Write a 1-2 sentence conclusion interpreting the results (you can simply restate the accepted hypothesis or explain it in another way) (1 point)

- Calculate the raw and standardized effect sizes (4 points total. 2 points for each measure: 1 for process/work, 1 for result)

- If the test was done with
*α*level of .10, using the same non-directional hypotheses, what would be the critical Z value from the Z table? What would be the result of the hypothesis test (in terms of rejecting or failing to reject the null hypothesis)? (2 points: 1 for critical Z, 1 for test result)

- Compare the hypothesis tests result when
*α*= .05 and when*α*= .10. Were the results the same? Why or why not? (1 point)