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HYPOTHESIS TESTING
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47. A bath soap manufacturing process is designed to produce a mean of 120 bars of soap per batch. Quantities over or under the standard are undesirable. A sample of ten batches show the following number bars of soap: 108, 118, 120, 122, 119, 113, 124, 122, 120, 123. SHOW ALL WORK.

a)    What is the sample mean
b)    What is the sample standard deviation
c)    Use Z or T test? And why?
d)    What is your hypothesis test
e)    At α = 0.05, what is the rejection rule when using the method you choose in (C)?
equal to 0.05
f)    Compute the value of the test statistic.
g)    What is the p-value

h)    What is your conclusion

48. Consider the following hypothesis test. Ho μ = 110. Ha: μ ≠ 110. A sample of 25 gives a sample mean of 115 and sample variance of 100. SHOW ALL WORK.

a)    Use Z or T test? And why?

b)At α = 0.05, what is the rejection rule?
.
c)Compute the value of the test statistic.

d)What is the p-value?
e)What is your conclusion?

49. Following is a portion of the computer output for a regression analysis relating y = maintenance expense (dollars per month) to x = usage (hours per week) of a particular brand of computer terminal. SHOW ALL WORK.
The regression equation is Y = 6.1092 + 0.8951X
Predictor          CoefStdev
Constant         6.1092      0.9361
X                      0.8951      0.1490
Analysis of Variance
Source                 DF          SS                    MS
Regression          1           1575.76         1575.76
Error                   8           349.14           43.64
Total                   9          1924.90
a)    Write and interpret the estimated regression equation
.
b)    What is the number of observations
c) Compute the F statistic and test the significance of the relationship at a 0.05 level of significance.
d) Predict monthly maintenance expense for any terminal that is used 25 hours per week

50.  Consider the model Y = f (X), where Y = Consumption of apple per person and X = Consumer income, hundreds of dollars per person. SHOW ALL WORK.
N = 10     ∑XY = 1803     ∑X = 44     ∑Y = 386      ∑X2 = 206     ∑Y2 = 18212

a) Find b1 and interpret

b) Find b0 and interpret

c) Write the equation

d) Find r2and interpret

e) Find SST
f) Find Se

g) Construct the 95% confidence interval for the mean of y when x = 7

h) Construct the 95% confidence interval for the individual value of y when x = 9

i) What is the consumption of apple per person when consumer income is \$500.

j) Interpret and show that you understand this regression equation (significant weight on this question)

53. A quality control engineer for a manufacturing plant wishes to determine whether the number of defective items manufactured during the week is approximately the same on each day. A week is selected at random, and the number of defective items produced with the same frequency each day. SHOW ALL WORK!

Day              Monday         Tuesday         Wednesday          Thursday          Friday
Number          32                    16                       23                         19                   40

a) What is your hypothesis
b) What is your x2
c) is the x2 value significant at 5% level of significance
d) Write the conclusion for this question
54. A survey at a ballpark show this selection of snacks purchased. At 10% significance level, is the snack chosen independent of the gender of the consumer? Show all work, do not use excel!
Snacks
Gender            Hot dog          Peanuts          Popcorn
Male                   12                     21                      19
Female              13                      8                       25

a) What is your hypothesis
.
b) What is your x2
c) is the x2 value significant at 10% level of significance

d) Write the conclusion for this question
We thus conclude that the type of snack is dependent on gender.
55. The following statistics were calculated in a regression analysis procedure.
DF = 7.0
b0= -10.8
b1= 3.0
Sb1 = 21.0

a) Test the null hypothesis that the slope of the regression line is zero at the .01 significant level. Show all work, do not use excel!

.

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