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4 years ago

A random sample is drawn from a population with mean μ = 66 and standard deviation σ = 5.5. use table 1.

1 answer:

7 0

A random sample is drawn from a population with mean μ = 66 and standard deviation σ = 5.5. use table 1.
a. is the sampling distribution of the sample mean with n = 16 and n = 36 normally distributed? yes, both the sample means will have a normal distribution. no, both the sample means will not have a normal distribution. no, only the sample mean with n = 16 will have a normal distribution. no, only the sample mean with n = 36 will have a normal distribution.
b. can you use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both sample sizes? yes, for both the sample sizes, standard normal distribution could be used. no, for both the sample sizes, standard normal distribution could not be used. no, only for the sample size with n = 16, standard normal distribution could be used. no, only for the sample size with n = 36, standard normal distribution could be used.
c. calculate the probability that the sample mean falls between 66 and 68 for n = 36. (round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

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Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the

krek1111 [17]

Answer:

The test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

H₀: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ = p₂.

Hₐ: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ ≠ p₂.

The two-proportion z-test would be used to perform the test.

A sample of n = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

$\hat p_{n}=\frac{6}{40}=0.15$

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

$\hat p_{s}=\frac{11}{40}=0.275$

The test statistic is:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

Compute the combined proportion P as follows:

$P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125$

Compute the test statistic value as follows:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

$=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$

Thus, the test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

8 0

3 years ago

-3/4 + 1/5 find each sum with out using a number line

Maru [420]

Might be terribly wrong since it's been a while that I've done fractions, but I got -11/20. Hope this helps!!!

8 0

3 years ago

The differential equation y′′=0 has one of the following two parameter families as its general solution: yyyy=C1ex+C2e−x=C1cos(x

svet-max [94.6K]

Answer:

y_c = 2 + 10*x

Step-by-step explanation:

Given:

y'' = 0

Find:

- The solution to ODE such that y(0) = 2, y'(0) = 10

Solution:

- Assuming a solution y = Ce^(mt)

So, y' = C*me^(mt)

y'' = C*m^2e^(mt)

- Back substitute into given ODE, we get:

y'' = C*m^2e^(mt) = 0

e^(mt) can not be equal to zero

- Hence, m^2 = 0

m = 0 , 0 - (repeated roots)

- The complimentary function for repeated roots is:

y_c = (C1 + C2*x)*e^(m*t)

y_c = C1 + C2*x

- Evaluate @ y(0) = 2

2 = C1 + C2*0

C1 = 2

-Evaluate @ y'(0) = 10

y'(t) = C2 = 10

Hence, y_c = 2 + 10*x

5 0

3 years ago

Scientists determined that Antarctica’s average winter temperature was -34.44 The difference between this temperature and Antarc

Slav-nsk [51]

-34.44 +49.44 = 15

The highest recorded temperature was 15 degrees.

6 0

3 years ago

Given the points (4, 5) and (-2, 8), find the slope of the line that passes through the points.

HACTEHA [7]

Answer: c

Step-by-step explanation:

Formula of slope of line :

m=y2-y1/x2-x1

m=8-5/-2-4

=-3/6

m=-1/2

7 0

3 years ago