6 The Department of Animal Husbandry at State University believes that adding cement to cattle feed will increase the cattle’s weight gain. The average weekly gain for State U cattle last year was 12.7 pounds. A sample of 30 cattle are fed cement-fortified feed with the following results: X = 14.1 pounds s=5.0 What can you tell the department?

To determine if adding cement to cattle feed will increase the cattle's weight gain, we can perform a hypothesis test using the average weight gain of the cattle.

Given:
- Population mean (μ): 12.7 pounds
- Sample mean ( \bar{X} ): 14.1 pounds
- Sample standard deviation (s): 5.0 pounds
- Sample size (n): 30

Null Hypothesis (H_0): μ = 12.7 (There is no significant difference in weight gain with cement-fortified feed.)
Alternative Hypothesis (H_1): μ > 12.7 (Weight gain is higher with cement-fortified feed.)

We can perform a one-sample Z-test to compare the sample mean with the population mean.

Calculate the test statistic Z:
Z = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}

Substitute the given values:
Z = \frac{14.1 - 12.7}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}
Z = \frac{1.4}{\frac{5.0}{\sqrt{30}}}

Now, we need to compare the calculated Z-value with the critical value at a chosen significance level (e.g., 0.05 for a 95% confidence level).

Using a Z-table or calculator, we find the critical Z-value for a one-tailed test at α = 0.05 is approximately 1.645.

Since the calculated Z-value falls in the rejection region (Z > 1.645), we reject the null hypothesis.

Therefore, we can conclude that there is evidence to suggest that adding cement to cattle feed increases the cattle's weight gain.

\boxed{Answer:} The department can conclude that adding cement to cattle feed likely increases the cattle's weight gain based on the test results.