Question

Music streaming services are the most popular wayto listen to music.Data gathered over the last 12 months show Apple Music was used by an average of 176 million households with a sample standard deviation of 0.55 million family units. Over the same 12 months Spotify was used by an average of 227 million families with asample standard deviation of 0.29 million. Assume the population standard deviations are not the same. Using a significance level of 002 test the hypothesis of no difference in the mean number of households picking either service. a. Find the degrees offreedom for unequal variance test. (Round down your answer to neerest whole number)

Answer 1

a) DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

           = ((0.55)^2/12 + (0.29)^2/12)^2/(((0.55)^2/12)^2/11 + ((0.29)^2/12)^2/11)

           = 17

b) At 0.02 significance level the critical values are t_0.01,17 = +/- 2.567

Reject H₀ if t < -2.567 or t > 2.567

c) The test statistic t = ($\dpi{100} \bar x1 - \bar x2$)/sqrt(s1^2/n1 + s2^2/n2)

                                 = (1.76 - 2.27)/sqrt((0.55)^2/12 + (0.29)^2/12)

                                 = -2.841

d) Since the test statistic value is less than the lower critical value (-2.841 < -2.567), so we should reject the null hypothesis.

Reject H₀. There is a significant difference in the mean number of households picking either variety of service to download songs.