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 1.65 million households with a sample standard deviation of 0.56 million family units. Over the same 12 months Spotify was used by an average of 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standard deviations are not the same. Using a significance level of .05, test the hypothesis of no difference in the mean number of households picking either service.

Answer 1

The average number of households using Apple Music is different from the average number of households using Spotify.

Hypotheses:

Null hypothesis (H0): There is no difference in the mean number of households picking either service. In other words, the mean number of households using Apple Music is equal to the mean number of households using Spotify.

Alternative hypothesis (HA): There is a difference in the mean number of households picking either service. In other words, the mean number of households using Apple Music is not equal to the mean number of households using Spotify.

Type of test:

This is a two-tailed test because we are interested in finding evidence that the mean number of households using Apple Music is different from the mean number of households using Spotify, regardless of whether the difference is positive or negative.

Test statistic:

The test statistic for this hypothesis test is the t-statistic, which is calculated as follows:

t =
`\frac{(\bar x_1_ - \bar x_2)} {√(((s_1^2/n1) + (s_2^2/n2)))}`

where:

`\bar x_1` is the mean number of households using Apple Music (1.65 million)

`\bar x_2` is the mean number of households using Spotify (2.2 million)

s1 is the sample standard deviation of households using Apple Music (0.56 million)

s2 is the sample standard deviation of households using Spotify (0.30 million)

n1 is the number of months of data for Apple Music (12)

n2 is the number of months of data for Spotify (12)

Plugging in the values, we get:

t = (1.65 - 2.2) /
`√(((0.56^2/12) + (0.30^2/12)))`

t = -1.96

Critical values:

The critical values for this hypothesis test are found using the t-distribution table with degrees of freedom (df) equal to the smaller of n1-1 and n2-1. In this case, df = 11.

At a significance level of 0.05, the two-tailed critical values are -2.20 and 2.20.

Decision:

Since the absolute value of the test statistic (1.96) is greater than the critical values (-2.20 and 2.20), we reject the null hypothesis.

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 1.65 million households with a sample standard deviation of 0.56 million family units. Over the same 12 months Spotify was used by an average of 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standard deviations are not the same. Using a significance level of .05, test the hypothesis of no difference in the mean number of households picking either service. Let the number of months = n.

Identify the hypotheses,which is the claim, the type of test, test statistic, critical value(s), decision, and conlcusion. Use the Omni calc to find the requested information.