A random sample of 100 observations from a quantitative population produced a sa

Question

A random sample of 100 observations from a quantitative population produced a sample mean of 27.8 and a sample standard deviation of 6.9. Use the p-value approach to determine whether the population mean is different rom 29. Explain your conclusions. Use 0.05 Round your test statistic to decima aces and your p-value to four decimal places.) 1-2. Null and alternative hypotheses: Ho: 29 versus Ha: = 29 Ho: = 29 versus Ha: 29 3. Test statistic: z = 4. p-value 5. Conclusion: Ho is not rejected. There is insufficient evidence to indicate that the mean is different from 29 Ho is not rejected. There is sufficient evidence to indicate that the mean is different from 29 Ho is rejected. There is sufficient evidence to indicate that the mean is different from 29. Ho is rejected. There is insufficient evidence to indicate that the mean is different from 29.

Explanation / Answer

Part 1-2

Null and alternative hypotheses are given as below:

H0: µ = 29 versus Ha: µ 29

Part 3

Test statistic = Z = (Xbar - µ) / [S/sqrt(n)]

We are given

Xbar = 27.8

S = 6.9

n = 100

Z = (27.8 – 29) / [ 6.9/sqrt(100)]

Z = -1.7391

Part 4

P-value = 0.0820

(By using z-table or excel)

Part 5

= 0.05

P-value > = 0.05

So, we do not reject the null hypothesis H0

H0 is not rejected. There is insufficient evidence to indicate that the mean is different from 29.

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