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 119 gallons per day and s = 5.3. at a = 0.05, is there enough evidence to say that the Old Farmer’s Almanac figure might no longer be correct?

To determine if there is enough evidence to say that the Old Farmer's Almanac figure might no longer be correct, we can conduct a hypothesis test. Here's how you can do it:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null hypothesis (H0): The average consumption of water per person per day is still 123 gallons (μ = 123).
- Alternative hypothesis (Ha): The average consumption of water per person per day is not 123 gallons (μ ≠ 123).

Step 2: Choose the significance level (α):
- In this case, the significance level is given as α = 0.05. This means we want our level of confidence to be 95%.

Step 3: Conduct the t-test:
- We will use the one-sample t-test because we are comparing the average consumption of water from a sample to a known population mean.

Step 4: Calculate the test statistic:
- The formula for the t-test is t = (x̄ - μ) / (s / √n), where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
- In this case, x̄ = 119, μ = 123, s = 5.3, and n = 16.
- Calculate t: t = (119 - 123) / (5.3 / √16)

Step 5: Determine the critical value(s):
- Since we have a two-sided alternative hypothesis (μ ≠ 123), we need to find the critical values for the upper and lower tails of the t-distribution.
- With α = 0.05 and df = n - 1 = 16 - 1 = 15, we can look up the critical value(s) in the t-distribution table or use software.
- For a two-tailed test, the critical values are t-critical = ±2.131.

Step 6: Compare the test statistic with the critical value(s):
- If the test statistic falls outside the range defined by the critical values, we reject the null hypothesis in favor of the alternative hypothesis.

Step 7: Make a decision and interpret the results:
- If the test statistic is outside the range defined by the critical values, we reject the null hypothesis. This means there is enough evidence to suggest that the Old Farmer's Almanac figure might no longer be correct.
- If the test statistic falls within the range defined by the critical values, we fail to reject the null hypothesis. This means there is not enough evidence to conclude that the figure in the Old Farmer's Almanac is incorrect.

By following these steps and calculating the t-test, you can determine if there is enough evidence to support the claim that the Old Farmer's Almanac figure might no longer be correct.