Question

Use the following for the next 6 questions. Lionfish are native to indo-pacific waters but the fish were introduced into the Atlantic in the 1990s. These spiny fish have huge appetites, feed on native species, and have andtypically have an average length of 13.5 inches. Recently, invasive Lionfish were found 300 feet below the water's surface off of the coast of Florida. There was some speculation that these fish were larger than previously observed. A random sample of 25 lionfish was obtained close to Fort Lauderdale. The length of each specimen was recorded in inches. The data below shows the distribution of fish lengths. Use the plot and the Routput to answer whether there is evidence to suggest the true mean length of Lionfish in this area near Florida is greater than the 13.5. Use a significance level of .05 and assume the underlying population is normal. Sample of 25 Lionfish One Sample t-test data: lionfishdata2 t = 3.1571, df = 24, p-value = 0.00213 alternative hypothesis: true mean is greater than 13.5 N 95 percent confidence interval: 14.77132 Inf sample estimates! 1 mean of x 10 15 20 25 30 16.275 29 I ength in Inches56. Describe the distribution using context and terms for the shape, center and spread of the distribution. Is there visual evidence the true mean may be more than 13.5 inches? 57. State the null and alternative hypothesis for the appropriate hypothesis test. 58. Checking Conditions. State each condition for Why is the condition met (or not met)? the test 59. The 95% confidence interval provided in the output is uninformative since it has one bound that is infinity. Calculate the 95% confidence interval provided x = 16.28 inches and s = 4.40 inches. 60. Using the software output and your calculated confidence interval above, summarize your conclusions in the context of the problem. Use the four-part conclusion method: Include a statement in terms of the alternative, whether or not you reject the null hypothesis based on the p-value and significance level, state and interpret the confidence interval and point estimate. Use a significance level of 0.05