A simple random sample of size nequals15 is drawn from a population that is normally distributed. The sample mean is found to be x overbarequals21.8 and the sample standard deviation is found to be sequals6.3. Determine if the population mean is different from 24 at the alpha equals 0.01 level of significance. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses. Upper H 0: ▼ mu sigma p ▼ less than equals greater than not equals 24 Upper H 1: ▼ sigma p mu ▼ equals not equals less than greater than 24 (b) Calculate the P-value. P-valueequals nothing (Round to three decimal places as needed.) (c) State the conclusion for the test. A. Do not reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance. B. Do not reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance. C. Reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance. D. Reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance. (d) State the conclusion in context of the problem. There ▼ is not is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
a)
| null hypothesis: HO: μ | = | 24 | |
| Alternate Hypothesis: Ha: μ | ≠ | 24 | |
b)
| population mean μ= | 24 | |||
| sample mean 'x̄= | 21.800 | |||
| sample size n= | 15 | |||
| std deviation s= | 6.300 | |||
| std error ='sx=s/√n=6.3/√15= | 1.6267 | |||
| t statistic ='(x̄-μ)/sx=(21.8-24)/1.627= | -1.3525 | |||
| p value = | 0.198 | from excel: tdist(1.352,14,2) | ||
c)
B. Do not reject Ho because the P-value is greater than the
alpha 0.01 level of significance.
d)
There is not sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
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