Question

A population is normal with a mean of 80 and a standard
deviation of 12.

A simple random sample of 50 is selected from the population. The
sample mean is 78. What is the p-value if you are conducting a
lower-tail (left tail) test?

Answer #1

Solution :

**Null and alternative hypotheses :**

The null and alternative hypotheses would be as follows :

**Test statistic :**

To test the hypothesis the most appropriate test is one sample z-test for mean. The test statistic is given as follows :

Where, x̅ is sample mean, μ is hypothesized value of population
mean under H_{0}, σ is population standard deviation
and n is sample size.

We have, x̅ = 78, μ = 80, n = 50 and σ = 12

The value of the test statistic is -1.1785.

**P-value :**

For left-tailed z-test the p-value is given as follows :

P-value = P(Z < value of the test statistic)

P-value = P(Z < -1.1785)

P-value = 0.1193

The p-value is 0.1193.

Please rate the answer. Thank you.

A population is normal with a mean of 80 and a standard
deviation of 12. A simple random sample of 50 is selected from the
population. The sample mean is 78. What is the p-value if you are
conducting a lower-tail (left tail) test?

Given a population with mean of 75 and standard deviation of 12.
A simple random sample of 36 is taken.
Find the following probabilities A. P (ഥX > 77 ) =
_____________ B. P ( 72 < ഥX < 78) = ______________
please help !!

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Sample Size
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Sample Mean
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Confidence Interval
Confidence Coefficient
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Upper Limit
Hypothesis Test
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