# MATHEMATICS

art A: Fill in the blank (1-26)

The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) __________________ concerning a (an) _______________ by examining the data contained in a (an) _______________ from that ____________________.

A hypothesis may be defined simply as __________________________________________.

There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.

The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis.

The _____________ hypothesis is the hypothesis that is tested.

If the null hypothesis is not rejected, we conclude that the alternative _________________.

If the null hypothesis is not rejected, we conclude that the null hypothesis _____________.

A Type I error occurs when the investigator _____________________________.

A Type II error occurs when the investigator _____________________________ .

The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________.

Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.

The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as____________ as or more _______ than that actually obtained is less than or equal to , the null hypothesis is____ _________.  Otherwise, the null hypothesis is ______________________ .

The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ____________ for the ________________test.

When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of σ2 , the test statistic is __________________________________.

When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a unknown variance, the test statistic is _____________________________________.

The null hypothesis contains a statement of __________________________________.

The statement  µ ≥  0 is an inappropriate statement for the ____________ hypothesis.

The rejection region consists of those values of the ______________ that will cause rejection of the null hypothesis.

The null hypothesis and the alternative hypothesis are ____________ of each other.

Given  ,  H0: µ= µ0, then Ha : ___________________________________ .

Given H0: µ ≤ µ0, then Ha : ___________________________________ .

Given H0: µ ≥ µ0, then Ha : ___________________________________ .

A statement of what you wish to conclude goes in the ______________.

A market analyst believes that more than 30% of the adults in a certain area regularly read a certain magazine.  The analyst wishes to conduct a hypothesis test to see whether this belief will be supported.  The appropriate statistical hypotheses are: __________________.

Given: H0: µ ≥ 50;  Ha: µ < 50; α  = 0.05.  A simple random sample of size 64 is drawn from a non-normally distributed population.   X ̅= 45, s2 = 256.  The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution.

Given: H0: µ= 100;  Ha: µ ≠ 100;   α = 0.03;  computed z = 2.25,  p = 0.0244.  The null hypothesis should reject because __________________________________________.

Part B: Use questions number 27-50 from page 9-54 to 9-57 to write your answer below (27-50).

273543

283644

293745

303846

313947

324048

334149

344250

Part C: Please fill in the blank and answer the following questions (51-53).

Use problem 14 on page 14-13 to fill in the table and answer the following questions.

SourceSSdfMSF

Treatments________________

Error____________

Total________

a) What is the hypothesis being tested in this problem?

b) In the above ANOVA table, is the factor significant at the 5% level?

c) Number of observations?

Use problem 16 on page 14-13 to fill in the table and answer the following questions.

SourceSSdfMSF

Treatments________________

Error____________

Total________

a) What is the hypothesis being tested in this problem?

b) In the above ANOVA table, is the factor significant at the 5% level?

c) Number of observations?

If R^2=0.95, n=11, and ∑▒〖〖(Y-Y ̅)〗^2=100,〗 what is S_e^2? (Single Regression model)

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