# Test of hypothesis

9.53 On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof. Hardtack that he is really a 90+ performer but this sample just happened to fall below his true performance level. (a) State an appropriate pair of hypotheses. (b) State the formula for the test statistic and show your decision rule using the 1 percent level of significance. (c) Carry out the test. Show your work. (d) What assumptions are required? (e) Use Excel to find the p-value and interpret it.

9.57 A sample of 100 one-dollar bills from the Subway cash register revealed that 16 had something written on them besides the normal printing (e.g., "Bob _ Mary"). (a) At · = .05, is this sample evidence consistent with the hypothesis that 10 percent or fewer of all dollar bills have anything written on them besides the normal printing? Include a sketch of your decision rule and show all calculations. (b) Is your decision sensitive to the choice of ·? (c) Find the p-value.

9.65 A consumer agency tested 290 hams, finding that 64 were underweight. (a) Construct a 95 percent confidence interval for the true percent of underweight hams. (b) If the goal is to reduce the incidence of underweight hams to 25 percent or less, does this sample show that the goal is being achieved? (c) Explain how this confidence interval is equivalent to a two-tailed test at · = .05. (Data are from Detroit Free Press, March 9, 1999, p. 2A.)

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9.53 On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof. Hardtack that he is really a 90+ performer but this sample just happened to fall below his true performance level. (a) State an appropriate pair of hypotheses. (b) State the formula for the test statistic and show your decision rule using the 1 percent level of significance. (c) Carry out the test. Show your work. (d) What assumptions are required? (e) Use Excel to find the p-value and interpret it.

Calculate Mean and Standard deviation of the sample

80 85 95 92 89 84 90 92

Mean and standard deviation

X= X^ 2 =

80 6400

85 7225

95 9025

92 8464

89 7921

84 7056

90 8100

92 8464

Total= 707 62655

n=no of observations= 8

Mean= 88.375 =707/8

variance={summation of X ^2 - n(Mean) 2 }/(n-1)= 24.8393 =(62655-8*88.375^2)/(8-1)

standard deviation = square root of Variance= 4.9839 = square root of 24.8393

(a) State an appropriate pair of hypotheses.

Null Hypothesis: Mean Score= 90

Alternative Hypothesis: Mean Score< 90

(b) State the formula for the test statistic and show your decision rule using the 1 percent level of significance.

Significance level= a (alpha) = 0.01 or 1%

No of tails= 1

Since sample size= 8 < 30

and we are estimating the population standard deviation from sample standard deviation

we will use t distribution

Sample statistic:

t=(sample mean- M )/s x

Critical value

t at the 0.01 level of significance and 7 degrees ...

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Answers to 3 questions on hypothesis testing