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MariettaO [177]
3 years ago
12

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to det

ermine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?
Mathematics
1 answer:
Maru [420]3 years ago
4 0

Answer:

0.077994

Step-by-step explanation:

Given that the owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club.

H_0: Mean = 30\\H_a: Mean >30

(Right tailed test)

Sample size = n=250

Sample mean = 30.45

Mean difference =30.45-30=0.45\\

Sample std dev s = 5

Sample std error = \frac{5}{\sqrt{n} } =\frac{5}{\sqrt{250} } \\=0.3163

Test statistic = Mean diff/std error = =\frac{0.45}{0.3163} =1.423

Since population std deviation is not know we use t test

p value = 0.077994

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at maximum speed, an airplane travels 1720 miles against th wind in 5 hours. Flying with the wind, the plane can travel the same
iragen [17]

Answer:

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

  • d = 1720
  • x = plane's speed
  • y = wind speed
  • t1 = 5 hours
  • t2 = 4 hours.

Substitution

  • d = (x + y) * t
  • 1720 = (x + y) * 4
  • 1720 = (x - y) * 5

Since the two distances are the same, you can equate the right hand sides.

  • (x + y) * 4 = (x - y)*5              Remove the brackets.
  • 4x + 4y = 5x - 5y                  Add 5y to both sides
  • 4x + 4y + 5y = 5x - 5y + 5y  Combine all the terms.
  • 4x + 9y = 5x                          Subtract 4x from both sides
  • 9y + 4x - 4x = 5x - 4x           Combine
  • 9y = x

Now use one of the given equations with the distance

  • 1720 = (x + y)*4           Substitute 9y for x
  • 1720 = (9y + y) *  4      Combine
  • 1720 = 10y * 4             Multiply the right
  • 1720 = 40y                  Divide by 40
  • 1720/40 = 40y/40      Do the division
  • 43 = y                          y = wind speek
  • 9y = x                          x = 9*y  
  • 9*43 = x
  • x = 387 miles per hour.
4 0
3 years ago
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