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Luba_88 [7]
2 years ago
15

Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved th

e mean listening time. It was discovered that the mean listening time for a sample of 10 men was 32 minutes per day. The standard deviation was 19 minutes per day. The mean listening time for a sample of 16 women was also 32 minutes, but the standard deviation of the sample was 9 minutes. At the 0.02 significance level, can we conclude that there is a difference in the variation in the listening times for men and women?
Mathematics
1 answer:
trasher [3.6K]2 years ago
7 0

Answer:

The null and alternative hypotheses are:

H_{0}:\sigma_{men} = \sigma_{women}

H_{a}:\sigma_{men} \neq \sigma_{women}

Under the null hypothesis, the test statistic is:

F=\frac{\sigma^{2}_{men}}{\sigma^{2}_{women}}

       =\frac{19^{2}}{9^{2}}

       =\frac{361}{81}

       =4.46

Therefore, the test-statistic is F=4.46

 Now the F critical value at 0.02 significance level for df1 = 10- 1 =9 and df2 = 16 - 1 =15 is:

F_{critical} = 3.303

Since F statistic is greater than the F critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that there is a difference in the variation in the listening times for men and women.


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The measure of the​ angle's supplement is 60
Sever21 [200]

Answer:

80°

Step-by-step explanation:

Let the angle be x then four times it's complement plus 60, that is

4(90 - x) + 60 ← is it's supplement

Supplementary angles sum to 180°

Sum the angle and it's supplement and equate to 180

x + 4(90 - x) + 60 = 180 ← distribute and simplify left side

x + 360 - 4x + 60 = 180

- 3x + 420 = 180 ( subtract 420 from both sides )

- 3x = - 240 ( divide both sides by - 3 )

x = 80

The required angle = x = 80°

supplement = 4(90 - 80) + 60 = 4 × 10 + 60 = 40 + 60 = 100°

4 0
2 years ago
Jon ran around a track that was 1\8 of a mile long.He ran around the track 24 times.How many miles did Jon run?
balandron [24]

Answer:

3 miles

Step-by-step explanation:

5 0
3 years ago
Tell whether the sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive
navik [9.2K]

Answer:

The explicit formula

a_n = 3 +0.25 (n-1)

The recursive formula

a_1 = 3                            for n=1

a_n = a_ {(n-1)} +0.25     if n>1

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

a_n = a_1 + d (n-1)

Where d is the constant difference between the terms.

d = 0.25

a_1 is the first term of the sequence.

a_1 = 3

So

a_n = 3 +0.25 (n-1)

Finally, the recursive formula is:

a_1 = 3\\\\a_n = a_ {(n-1)} +0.25

8 0
2 years ago
66 bats were sold. Some were sold for $42 each the rest were sold for $30 each. The total sales were$2,460. Write and solve a sy
Phoenix [80]

Answer:

40 bats sold for $42

26 bats sold for $30

Step-by-step explanation:

x + y = 66

42x + 30y = 2460

solve first equation for y and plug in for y in second equation

42x + 30 (66 - x) = 2460

x = 40

y = 66- 40 = 26

5 0
3 years ago
Help with this question
snow_tiger [21]

Answer:

c

Step-by-step explanation:

just take out the brackets and add the like terms.

6 0
3 years ago
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