Assume that, on average, healthy young adult’s dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes. (a) Use t to test the null hypothesis at the .05 level of significance (b) If appropriate (because the null hypothesis has been rejected), construct a 95 per-cent confidence interval and interpret this interval
Answers
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 90
For the alternative hypothesis,
µ < 90
If drinking coffee just before going to sleep affects the amount of dream time, then the amount of dream time would be less than 90 minutes. It means that it is left tailed.
Since the number of samples is 28 and no population standard deviation is given, the distribution is a student's t.
Since n = 28,
Degrees of freedom, df = n - 1 = 28 - 1 = 27
t = (x - µ)/(s/√n)
Where
x = sample mean = 88
µ = population mean = 90
s = samples standard deviation = 9
t = (88 - 90)/(9/√28) = - 1.176
We would determine the p value using the t test calculator. It becomes
p = 0.124
Since alpha, 0.05 < than the p value, 0.124, then we would not reject the null hypothesis. Therefore, At a 5% level of significance, the sample data did
not show significant evidence that drinking coffee just before going to sleep affects the amount of dream time.
Related Questions
If 12 gallons of water are divided evenly into 7buckets, how much will be in each bucket?
Consider the statement p:x+9=10.which of the following is a equivalent statement
HELP PLEASE!!! The following graph shows farm sector production in billions of dollars from 1994–2003. One line shows the yearly production and the other shows the average over the time span. According to the graph, in which 3 years were the values of farm sector production closest to the average for the 10 years shown?A): 1994, 1996, 1998B): 1996, 1998, 2000 C): 1998, 2000, 2002 D): 2000, 2002, 2004
HELP ME PLZZZZZZ IM BEGGING YOU
Thanks for any help
Answers
Answer:
20/18
Step-by-step explanation:
Answer:10/9 exact form mixed # 1 1/9
Step-by-step explanation:reduce the expression, if possible, by cancelling the common factors.
Answers
Answer:
18√2
Step-by-step explanation:
The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.
36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle
Answers
Answer:
D. 11.6 cm
Step-by-step explanation:
The missing length of the right angled triangle can be calculated using Pythagorean Theorem as shown below:
Where,
a = x cm
b = 11 cm
c = 16 cm
Thus:
(nearest tenth)
Answer:
Step-by-step explanation:
11.16
Answers
Answer:
14 to the 10th power
Step-by-step explanation:
If two exponents have the same base, you can subtract them if they're being divided.
In your case:
14 to the 15th power/14 to the 5th power
We can subtract:
15 - 5 = 10
So our final answer would be:
14 to the 10th power
(the fourth answer)
Hope this helps!
Answer:
14¹⁰
Step-by-step explanation:
14¹⁵ divided by 14⁵ equals 14¹⁰
Answers
Answer:
Cai's Would Be Bluer
Step-by-step explanation:
Since 2/5 is 40% and 5/11 is 45% Cai's would be bluer!
Final answer:
Cai's paint will be bluer because she used a higher percentage of blue paint (45.45%) in her mix compared to Casho who used 40% blue paint.
Explanation:
In order to determine whose paint mix will be bluer, we must compare the ratio of blue to red paint in each student's mix. Cai mixes 5 cups of blue and 6 cups of red paint. Casho mixes 2 cups of blue and 3 cups of red paint. We find the percentage of blue paint by dividing the amount of blue paint by the total amount of paint and then multiplying by 100. For Cai, it would be (5 / (5 + 6)) * 100 = 45.45% blue. For Casho, it would be (2 / (2 + 3)) * 100 = 40% blue. Thus, Cai's purple paint will be bluer because it has a higher percentage of blue paint.
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Answers
The scale factor of the dilation is approximately 1.25.
To find the scale factor of the dilation, we need to compare the corresponding side lengths of the original figure and the dilated figure.
Let's consider the two corresponding side lengths:
Original side: EN = 16 units
Dilated side: BN = 20 units
The scale factor (k) of the dilation is the ratio of the corresponding side lengths in the dilated figure to the original figure. It can be calculated using the formula:
Scale factor (k) = Dilated side length / Original side length
Substituting the given values:
k = 20 / 16 ≈ 1.25
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