Week 5 HW One-Sample t-test (song length)

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Fort Lewis College *

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Statistics

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May 3, 2024

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Week 5 HW One-Sample t-test (Song Length) Background Information: Quartz (qz.com) claims that the average song length is 3.5 minutes long. 30 song titles from Billboard’s Top 100 during the week of July 6 th were randomly selected (using random number generator). Then Spotify was used to gather the length of each song, in minutes. Complete the six-step hypothesis test process to determine whether the mean song length differs from the claimed 3.5 minutes average. Show and label all steps and include all relevant SPSS output. Let alpha=0.01. 1: Research Question Is there sufficient evidence to indicate that the mean song length differs from the claimed 3.5 minutes average? 2: Statistical Hypotheses 0 : H 3.5 1 : H 3.5 Test used: _ One Sample t-test ____ 3: Decision Rule Let alpha = 0.01, two-tailed. I will reject the null hypothesis if p < 0.01 and I will fail to reject null hypothesis if p > 0.01. 4: Assumptions, Calculations, SPSS output, etc. (This step requires that you include one SPSS histogram, two SPSS tables, and show where you have checked your assumptions, as well as whether they have been met.) - Histogram approximately Normal- YES, The histogram shows a curve bell shape which shows a normal histogram. Follows normal distribution. - Histogram has outliers- YES. The outliers are on the left side of the histogram. Thus, the assumptions are met. 4.18 3.67 2.95 2.63 3.97 3.63 3.68 3.35 2.93 3.02 3.05 2.47 2.62 2.95 3.67 1.92 3.57 2.65 3.84 3.82 3.33 3.03 3.22 3.23 3.80 3.32 3.18 2.50 2.90 2.63

Week 5 HW One-Sample t-test (Song Length) 5: Statistical Decision Since the p-value= .003, then I will reject the null hypothesis, because SPSS p- value < 0.01. .003 < 0.01 which is why I will reject the null hypothesis.

Week 5 HW One-Sample t-test (Song Length) 6: Informal Interpretation (Be sure that you consult the grading rubric, as well as your One Sample t-test Notes, and your Maze assignment for all that is required in this step. Your interpretation should be in YOUR own words, even if you worked with a partner/group.) Our study finds statistical evidence that the mean song length differs from the claimed 3.5 minutes average, it is lower than the claimed average. A One sample t-test with alpha= 0.01, two-tailed, was used in out study. Using the data provided, we found a mean of 3.1903 minutes. This means that the mean is lower than the claimed value of 3.5 minutes. t (29) = -3.214, p=.003 (p<0.01), two-tailed, 99% Cl [-.5752, -.0441]. I am 99% confident that the mean song length differs between .5752 minutes and .0441 minutes lower than the claimed mean of 3.5 minutes. The mean difference between the two means is .30967 minutes. What do you believe your score should be on this assignment? I believe that I should get a score of 47 out of 50, because I included all the things that were required by the assignment, and I tried to follow the criteria in the rubric as best as possible. I also had to use the One Sample t-test M&M Hypothesis test as an example because I was gone for the beginning of this chapter, and I am still trying to catch up so I may have some questions before the next exam. I would prefer a score of 50 out of 50 but I would be happy with a 47 out 50.

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