Question

h-l please. also, for part (g) the interval is [6.71,8.95]

A scientist studying snow crabs wanted to determine the relationship between crab shell width and amount of edible meat in the crab. Specifically, the objective was to "predict" the amount of edible meat from shell width (making Y the amount of edible meat and X the shell width). He caught 16 snow crabs and measured shell widths (in inches) before opening them up to measure the weight (in ounces) of the edible meat contained within each crab. Shell Width Weight Shell Width Weight 2.8 2.5 3.0 4.0 5.6 5.0 6.0 7.7 5.7 8.8 7.8 3.8 9.2 9.0 10.0 15.2 12.0 3.5 3.5 3.4 3.1 2.9 4.0 4.9 4.5 12.8 16.3 (g) Calculate and interpret within the context of this experiment a 2 sided 95% confidence interval for expected weight of the edible meat (in ounces) for snow shell crabs having shell width 3.25 inches. (h) Set up the appropriate null and alternate hypotheses to determine whether or not one can expect 9 ounces of edible meat in snow crabs having shell width 3.25 inches, and use the confidence interval of part (g) to perform the test Is it necessary to put a bound on the probability of making a Type I error? Remember, for a two tailed test, "not equal to" always goes into the alternate hypothesis () Calculate the P-value for the test in part (h G) The research hypothesis is that an increase of 0.25 inches in snow crab shell width will produce a corresponding increase of more than 0.875 ounces in edible meat, on average. Set up the appropriate null and alternate hypotheses. Calculate the P value and use it to perform the test. (k) Construct the appropriate confidence interval and use it to perform the hypothesis test of part 6G) with PI)-0.05 (1) Construct and interpret a 95% confidence interval (matching the one in part (k) in type [i.e. upper, lower, or two sided] for the change in expected weight of edible meat (in ounces) for an increase of 0.25 inches in snow crab shell width. Now use this confidence interval to perform the hypothesis test of part G)

Answer 1

The P.Value for the above H-1 is P.Value =0.000

and the output is given below

  
Regression Analysis: Weight versus Shell Width

The regression equation is
Weight = - 8.29 + 4.96 Shell Width

Predictor Coef SE Coef T P
Constant -8.288 2.599 -3.19 0.007
Shell Width 4.9562 0.7187 6.90 0.000

S = 1.88237 R-Sq = 77.3% R-Sq(adj) = 75.6%

Analysis of Variance

Source DF SS MS F P.value
Regression 1 168.49 168.49 47.55 0.000
Residual Error 14 49.61 3.54
Total 15 218.10

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 7.820 0.520 (6.705, 8.934) (3.631, 12.008)

Values of Predictors for New Observations

Shell
New Obs Width
1 3.25