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Vitek1552 [10]
3 years ago
9

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.
Mathematics
1 answer:
marysya [2.9K]3 years ago
3 0

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

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stich3 [128]

Answer:

190.9 in³

Step-by-step explanation:

Whenever one is asked to find how much(quantity of something) a certain container can hold,all you need to understand is that you are been asked about the volume of that container

We all know that the volume of a sphere is 4/3 × 22/7 × r³

And since we are dealing with a container in the shape of half a sphere,the volume of that container will now be volume of a sphere divided by 2

If the formula that was given initially was divided by 2,the new formula will look like this:

4/6 × 22/7 × r³

And we have the diameter but not the radius and we know that to find the radius, all we need to do is to divide the diameter by 2

That is 9/2 = 4.5

Putting the values in the formula,we can now derive the volume of that sphere

4/6 × 22/7 × 4.5³

= 190.9 in³ of soil

5 0
3 years ago
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How many gallons of a 90% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 80% antif
lozanna [386]

Answer:

540

Step-by-step explanation:

Amount of antifreeze in the 90% solution + amount of antifreeze in the 20% solution = amount of antifreeze in the 80% solution

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Answer:

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Step-by-step explanation:

Hope this helps :)

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Find the population mean or sample mean as indicated. Sample: 19, 15, 6, 11, 24 Compute the sample mean for this data set. Selec
yKpoI14uk [10]

Answer:

\overline{x}=15

Step-by-step explanation:

the mean is given by:

\overline{x} = \dfrac{\sum\limits_{i=1}^n x_i}{n} \quad\text{or}\quad \dfrac{\text{sum of all items}}{\text{number of items}}

In our case this is:

\overline{x} = \dfrac{19+15+6+11+24}{5} \Rightarrow \dfrac{75}{5}\\\\\overline{x} = 15\\\\

side note: the main difference between sample mean and population mean is in the 'context'. However, the method to calculate them is the same.

By context I mean: if this the items are taken from some larger category for example: the ages of a few 'students' from a 'class'. Here 'students' are the sample from a larger set that is 'class'. The mean of the 'few students' will be called sample mean. In contrast, if we take the mean of the ages of the whole class then this is called population mean. (population mean == mean of the whole set)

In our case we aren't told exactly where these numbers come from, is this the whole set or a sample from it, the lack of context allows us to assume that the mean can either be population mean or sample mean. So we can safely use any symbol \mu or \overline{x}.

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3 years ago
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natima [27]

Answer:

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Step-by-step explanation:

It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).

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  y = mx + b

where m is the slope and b is the y-intercept.

The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.

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