Question

Place your answers on the templates provided. Show your work. Directions: 1. A doctor knows that muscle mass decreases with age. To help him understand this relationship in women, the doctor selected women beginning with age 40 and ending with age 80. The data is given in the table below. x is age, y is a measure of muscle mass (the higher the measure, the more muscle mass). Use your calculator to make a scatter plot that shows how age helps explain muscle mass. Does there appear to be a linear relationship? Find the Pearson sample correlation coefficient, r. What does r tell you about the strength of the relationship? At the 1% level of significance, perform a hypothesis test to test the significance of the correlation coefficient. hypothesis Find the least squares regression equation. Interpret slope and y-intercept in context of the problem. Be sure to graph this regression equation within your scatter plot to make sure your equations appears to "best fit" the data. Predict the muscle mass for women aged 60 years. Is the predicted value in part d. an interpolated or extrapolated value? Explain. If the muscle mass of a woman was determined to be 58, what age does the model predict she would be? a. b. Use your scatter plot's shape to determine the form of the alternative c. d. e. f. g Would you trust the model's prediction for the value you calculated in part f? Why or why h. In order to help you have more "good faith" in your model, create a residual plot. You must not? plot the original x-values(AGE) along with the residuals as Y-values(Residual -y-y). Are there any patterns in the residual plot that would make you "second guess" your original assumption of linearity? (Age) (Muscle(Age) (Muscle Mass) Mass) 80 101 63 86 105 73 95 100 112 75 62 42 66 69 71 86 57

Answer 1

Solution:-

3)

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

Null hypothesis: The sample data fits the distribution of unloaded dice.

p₁ = p₂ = p₃ = p₄ = p₅ = p₆

Alternative hypothesis: At least one of the proportions in the null hypothesis is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 6 - 1
D.F = 5
(E_i) = n * p_i

Observed Outcome experiment ExpectedOrc-Erc1Erd 2.88 0.5 3.38 6.48 0.18 0.02 13.44 50 50 50 50 0) 50 62 45 (XI 32 47 51 300 2 3 4 Total


Er,c

X² = 13.44

X²_Critical = 15.09

Rejection region is X² > 15.09

р 0.01 1.581 4.743 7.906 11.07 14.23 Х2 15.09 17.39 20.55

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

Interpret results. Since the X²-value (13.44) does not lies in the rejection region, hence we failed to reject the null hypothesis.

From the above test we cannot conclude that the die is loaded.