The average number of pods on one of the farmer’s peanut plants is 145 pods with

Question

The average number of pods on one of the farmer’s peanut plants is 145 pods with a standard deviation of 100 pods. This year, after trying a new planting technique, the farmer took a random sample of 144 of the plants and finds the average number of pods to be 147.

1. State the null and alternative hypotheses to be tested?

2. Test null hypothesis at the 5% level of significance. Using the critical value approach, state the decision rule for the test?

3. Test null hypothesis at the 5% level of significance, using p value approach and state the decision rule for the test?

4. What do you conclude about the population mean?

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

1) Null hypothesis: = 145

Alternative hypothesis: 145

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 8.333

DF = n - 1 = 144 - 1

D.F = 143

t = (x - ) / SE

t = 0.24

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

2)

tcritical = 1.977

Critical region:-

1.977 > t > 1.977

Since t value (0.24) is less than the critical value, hence we cannot reject the null hypothesis.

3)

Since we have a two-tailed test, the P-value is the probability that the t statistic having 143 degrees of freedom is less than - 0.24 or greater than 0.24.

Thus, the P-value = 0.811

Interpret results. Since the P-value (0.811) is greater than the significance level (0.05), we cannot reject the null hypothesis.

4) From the above test we have sufficient evidence in the favor of the claim that population is same as sample mean.

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