Question

In 2017, the top 5 Pop artists (so n_pop = 5) sold a mean number of 358,200 albums (SD = 227,656), and the top 5 R&B/Hip-Hop artists (so n_RBH = 5) sold a mean number of 352,600 albums (SD = 109,061).

Assuming conventional alpha, what is the critical value for the analysis that will help us judge whether these group means are significantly different?

Answer 1

Since the number of data points is very less i.e. 5, we will use the t-test for analysis.

Conventional alpha = 0.05

N = 5

Degree of freedom = N - 1 = 4

Using the t-table , we find that the t score corresponding to and Degree of freedom = 4 is 2.776 which is the critical value

Using this critical value we will calculate the confidence interval corresponding to 0.05 alpha

For pop artist

N = 5

Mean = 358200

SD = 227656

Standard Error = = =

Confidence interval for mean number of albumbs sold for pop artists =

=

For R&B/Hip-hop artist

N = 5

Mean = 352600

SD = 109061

Standard Error = = =

Confidence interval for mean number of albumbs sold for pop artists =

=

Hence, we can see that using the critical value, the range for 95% of the HIP-HOP artists' album sold is more closer to the mean than that of the pop artist.

so, even with a very similar means for the number of albums sold, the range for the number of albums sold is much higher in the case of pop artists than hip-hop artists and thus we can say that the group means are significantly different.

Thank you.

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