234 5 7 8 910 Next Question 6 of 10 (1 point) View problem in a pop-us The Old F

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234 5 7 8 910 Next Question 6 of 10 (1 point) View problem in a pop-us The Old Farmer's Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 16 people and found that they used on average 120.8 gallons per day ands-53. At - 0.10, is there enough evidence to say that theOld Farmer's Almanac figure might no longer be correet? Use the P-value method. Assume the population is normally distributed. Use a graphing calculator Part 1 out of 4 State the hypotheses and identify the claim with the correet hypothesis. H 0: i (select) H1: (select) This hypothesis test is a (select) test. (select) (select)

Explanation / Answer

Solution:-

6)

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

Null hypothesis: = 123

Alternative hypothesis: 123

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 0.10. 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 = 1.325

DF = n - 1 = 16 - 1

D.F = 15

t = (x - ) / SE

t = - 1.66

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.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 15 degrees of freedom is less than -1.66 or greater than 1.66.

Thus, the P-value = 0.1178

Interpret results. Since the P-value (0.1178) is greater than the significance level (0.10), we cannot reject the null hypothesis.

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