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Sagot :
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, [tex]\overline {X}_1[/tex] = 1.73 million
The standard deviation, σ₁² = 0.46 million
The average number of households using Spotify, [tex]\overline {X}_2[/tex] = 2.17 million
The standard deviation, σ₂² = 0.33 million
The significance level = 0.01
Hypothesis testing with different population standard deviation
[tex]Z = \dfrac{\overline {X}_1 - \overline {X}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} +\dfrac{\sigma_2^2}{n_2}} }[/tex]
H₀: [tex]\overline {X}_1[/tex] ≠ [tex]\overline {X}_2[/tex]
H₁: [tex]\overline {X}_1[/tex] = [tex]\overline {X}_2[/tex]
[tex]Z = \dfrac{1.73- 2.17}{\sqrt{\dfrac{0.46^2}{12} +\dfrac{0.33^2}{12}} } = -2.6923[/tex]
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
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