Question

Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.73 million households with a sample standard deviation of 0.46 million family units. Over the same 12 months Spotify was used by an average of 2.17 million families with a sample standard deviation of 0.33 million. Assume the population standard deviations are not the same. Using a significance level of 0.01, test the hypothesis of no difference in the mean number of households picking either service.

Answer 1

Answer:

There is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service

Step-by-step explanation:

The parameters of the music streaming service are;

The average number of households using Apple Music, $\overline {X}_1$ = 1.73 million

The standard deviation, σ₁² = 0.46 million

The average number of households using Spotify, $\overline {X}_2$ = 2.17 million

The standard deviation, σ₂² = 0.33 million

The significance level = 0.01

Hypothesis testing with different population standard deviation

$Z = \dfrac{\overline {X}_1 - \overline {X}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} +\dfrac{\sigma_2^2}{n_2}} }$

H₀: $\overline {X}_1$ ≠ $\overline {X}_2$

H₁:  $\overline {X}_1$ = $\overline {X}_2$

$Z = \dfrac{1.73- 2.17}{\sqrt{\dfrac{0.46^2}{12} +\dfrac{0.33^2}{12}} } = -2.6923$

p-value for the test statistic = 2 × P(Z <-2.6923) = 2 × 0.00357 = 0.00714

Therefore, the p-value is less than the significance level, and it is therefore unlikely that the result will be observed under the null hypothesis

We therefore reject the null hypothesis and there is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service