Discuss the following:
Q1. A sample of 64 observations is selected from a normal population. The sample mean is 216, and the sample standard deviation is 15. Conduct the following test of hypothesis sing the .03 significance level.
H0: µ ≥ 220
H1: µ < 220
a. State the null and the alternate hypothesis
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value? Interpret it.
Q2. A sample of 42 observations is selected from one population. The sample mean is 102 and the sample standard deviation is 5. A sample of 49 observations is selected from a second population. The sample mean is 99 and the sample standard deviation is 6. Conduct the following test of hypothesis using the .04 significance level.
H0: µ1 = µ2
H1: µ1 ≠ µ2
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule
c. Compute the value of the test statistic
d. What is your decision regarding H0?
e. What is the p-value?
Q3. What is the critical value for a sample of eight observations in the numerator and six in the denominator? Use a two-tailed test and the .10 significance level.
Q4. The following is sample information. Test the hypothesis that the treatment means are equal. Use the .05 significance level.
Treatment 1 Treatment 2 Treatment 3
8 3 3
6 2 4
10 4 5
9 3 4
a. State the null hypothesis and the alternate hypothesis.
b. What is the decision rule?
c. Compute SST, SSE, and SS total.
d. Complete an ANOVA table.
e. State your decision regarding the null hypothesis.
Q5. The following sample observations were randomly selected.
X: 4, 5, 3, 6, 10
Y: 4, 6, 5, 7, 7
Determine the coefficient of correlation and the coefficient of determination. Interpret. Also, construct a regression equation for this sample data.
Q6. Given the following sample observations, develop a scatter diagram. Compute the coefficient of correlation. Does the relationship appear to be linear? Compute the standard error of the estimate. Which model produces the most accurate estimates? Explain your decision (hint: use the models' computed values to support your decision).
X1: 8 16 12 20 18
Y1: 58 247 153 100 341
X2: 8 15 13 21 19
Y2: 61 250 154 101 360