Question

Sara is a big hip-hop music fan. Her friend Matt is a big rap music fan. They each have a huge library of songs in their digital music libraries. They each randomly sample 50 songs from their libraries and record the lengths of the songs selected. The average of the selected hip-hop songs was x1

Answer 1

The critical value is 1.99 and the null hypotheses is μ - μ₂ = 0 and alternative hypotheses for this test is μ - μ₂ ≠ 0.

According to the statement

we have given that the sample of songs is 50. and the average of hip hop is μ₂.

For this purpose, we know that the

Sara and matt would like to know if the average length of the hip hop songs say μ₁ differ from the average of the hip hop songs say μ₂. It means μ₁ ≠ μ₂.

so, The null and alternative hypothesis value are:

H(null) = μ - μ₂ = 0 And

H (alternative) = μ - μ₂ ≠ 0.

From this it is clear that the this the value of hypothesis.

So,

Now, Let the degree of freedom be a x.

Then

At $\alpha = 0.05$ then the value of k is 80,.

Then the critical value is

$t = (\frac{\alpha }{2} , k) = 1.99$

Here the critical vale is 1.99.

So, The critical value is 1.99 and the null hypotheses is μ - μ₂ = 0 and alternative hypotheses for this test is μ - μ₂ ≠ 0.

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Question:

Sara is a big hip-hop music fan. Her friend Matt is a big rap music fan. They each have a huge library of songs in their digital music libraries. They each randomly sample 50 songs from their libraries and record the lengths of the songs selected. The average of the selected hip hop songs was *, - 245 seconds with a sample standard deviation of 5 seconds. The average of the selected rap songs was X - 275 seconds with a sample standard deviation of 6 seconds. They would like to know if the average length of hip-hop songs is different than the average length of rap songs. (a) What are the appropriate null and alternative hypotheses for this test? (b) Assume for purposes of this study, the degrees of freedom are 80. At a 5% significance level, what is the critical value for the test?

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