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.

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