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Researchers are studying two populations of wild horses living in the western regions of a country. In a random sample of 32 horses taken from the first population, the mean age of the sample was 21 years. In a random sample of 41 horses from the second population, the mean age of the sample was 19 years. Is the sampling distribution of the difference in sample mean ages approximately normal?

A Yes, because the two populations of wild horses can be modeled by a normal distribution.
B Yes, because the samples were selected at random.
C Yes, because the sample sizes are both greater than 30.
D No, because the populations are not normal.
E No, because the difference in sample mean ages was not 0.

Respuesta :

Answer:

Correct option: (C) Yes, because the sample sizes are both greater than 30.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

For the first sample, the sample size of the sample selected is:

n₁ = 32 > 30

Ans for the second sample, the sample size of the sample selected is:

n₂ = 41 > 30

Both the samples selected are quite large.

So, the Central limit theorem can be used to approximate the distribution of of the two sample means.

Ans since the distribution of the two sample means follows a normal distribution, the difference of the two means will also follows normal distribution.

Thus, the correct option is (C).

C Yes, because the sample sizes are both greater than 30.

The following information should be considered;

  • Given that, [tex]n_1 = 32[/tex] and [tex]n_2 = 41[/tex]
  • Here both sample size should be more than 30.
  • By applying the central limit theorem, sampling distribution of difference should be normal.
  • Therefore, the third option is correct.

learn more; https://brainly.com/question/1368131?referrer=searchResults

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