Subject Code : STATS1000
Assessment Task:

 


1. The one-sample t-test in SPSS
This question must be typed in Word
Fifty songs were randomly selected from Spotify and their duration measured. The data is given in songs.sav on MyUni.
This data has one variable: • seconds: the duration calculated in a total number of seconds. A music critic reckons that all good songs are 4 minutes long. In this question, we will test if the data from Spotify is consistent with this statement.
(a) First, examine the distribution of the total seconds by doing the following:
i. Produce a histogram of the variable seconds in SPSS and include in your assignment.
ii. Describe the distribution of total seconds.
(b) Perform a one-sample t-test of the null and alternative hypotheses
H0: µ = 240, Ha: µ 6= 240, where µ is the true population mean duration of songs in seconds on Spotify.
To do this, complete the following steps:
i.
Perform a one-sample t-test in SPSS and include the output in your assignment.
ii. State the value of the test statistic.
iii. State the P-value.
iv. State the distribution of the test statistic if the null hypothesis is true.
v. State whether you reject or retain the null hypothesis at the 5% signi?cance level? Justify your decision.
(c) Using your SPSS output, calculate a 95% con?dence interval for the mean song duration in seconds. Interpret this interval in context.
(d) Check the assumption of normality of the sample mean with the following steps:
i. Produce a normal QQ-plot of the total seconds and include in your assignment.
ii. Using the normal QQ-plot, decide if the assumption of normality is reasonable for total seconds. If not, which theorem, that states that the sample mean is approximately normally distributed for large sample sizes, could be used to justify the use of the t-test?

2. Two-sample T-test in SPSS
For full marks, this question must be typed in Word, all required SPSS output should be included and captioned. The Bechdel test1 is used to classify movies according to the following criteria: • The movie has to have at least two women in it, • who talk to each other, 
about something besides a man. Does passing the Bechdel test have an e?ect on a movie’s pro?ts?
The dataset Bechdel.sav was obtained from http://fivethirtyeight. com/. The data has been ?ltered such that only movies that were released from 2010 onwards are included. The column Bechdel indicates whether the movie passes or fails the Bechdel test, and the column profit is calculated as gross−budget budget, where all amounts are converted to 2013 US dollars to account for in?ation. The units of pro?t are a proportion of the budget.
(a) Import the dataset into SPSS and produce a panel histogram of profit against Bechdel (include your captioned plot in your ?nal submission). What is the shape of the distribution of pro?t for each type of movie? Does pro?t look to be normally distributed?
(b) Perform a two-sample T-test in SPSS (include your output in your submission). Note you should de?ne Group 1 as PASS and Group 2 as FAIL.
i. Write down appropriate null and alternative hypotheses for the two-sample T-test. Remember to de?ne any parameters used.
ii. What is the observed value of the test statistic?
iii. What is the distribution of the test statistic if the null hypothesis is true? Note: use the SPSS output for the degrees of freedom.
iv. What is the P-value?

 

This Statistics Assessment has been solved by our Statistics Experts at UniLearnO. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.

Eureka! You've stumped our genius minds (for now)! This exciting new question has our experts buzzing with curiosity. We can't wait to craft a fresh solution just for you!

  • Uploaded By : Ariana
  • Posted on : November 13th, 2018

Whatsapp Tap to ChatGet instant assistance