Arandom sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviation of 8.3.

use the p-value approach to determine whether the population mean is different from 24.

explain your conclusions. (use α = 0.05.)

state the null and alternative hypotheses. h0: μ = 24 versus ha: μ ≠ 24 h0: μ = 24 versus ha: μ > 24 h0: μ ≠ 24 versus ha: μ = 24 h0: μ = 24 versus ha: μ < 24 h0: μ < 24 versus ha: μ > 24

find the test statistic and the p-value. (round your test statistic to two decimal places and your p-value to four decimal places.) z = p-value = state your conclusion.

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

We use Two-tailed z test to perform this hypothesis.

Formula:

Putting all the values, we have

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now,

Since,  the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

step-by-step explanation:

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