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satela [25.4K]
3 years ago
13

A new family has moved in next door. You know the family has two children. What is the probability that both children are boys?

Mathematics
1 answer:
Snezhnost [94]3 years ago
8 0
There is a 50% probability.
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Consider the following hypothesis test: H0: μ1 - μ2 = 0 Ha: μ1 - μ2 ≠ 0 There are two independent samples taken from the two pop
nlexa [21]

Answer:

The value of the test statistic is z = 1.78

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Sample 1:

\mu_1 = 110, s_1 = \frac{7.2}{\sqrt{81}} = 0.8

Sample 2:

\mu_2 = 108, s_2 = \frac{6.3}{\sqrt{64}} = 0.7875

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

Distribution of the difference:

X = \mu_1 - \mu_2 = 110 - 108 = 2

s = \sqrt{s_1^2+s_2^2} = \sqrt{0.8^2+0.7875^2} = 1.1226

What is the value of the test statistic?

z = \frac{X - \mu}{s}

z = \frac{2 - 0}{1.1226}

z = 1.78

The value of the test statistic is z = 1.78

5 0
3 years ago
Graph the image of the given triangle after a rotation of 180° about the origin
denis-greek [22]

Answer:

The bottom point is at (-1, 1) the right point is at (6,-2) and the left point is at (-5,4)

Step-by-step explanation:

7 0
2 years ago
The level of significance is the a. same as the p-value. b. maximum allowable probability of Type I error. c. same as the confid
Temka [501]

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

5 0
2 years ago
Help ASAP! Will vote brainliest!
romanna [79]
The answer I. C : negative correlation, and casualty
5 0
2 years ago
What answer represents this number in scientific notation.I need help fast. Will mark who ever answer fastest brainiest.
MrRa [10]
D, look it up on Math. Way it tells you mostly everything you can know about math.
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3 years ago
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