The following is sample information. We are asked to test the hypothesis at the 5% significance level that the treatment means are equal. Assume that the treatment results for each type of treatment are normally distributed with equal standard deviations (and variances).Treatment ITreatment IITreatment III9131072091114159131412 15101.) State the null hypothesis.A.) ?0H0 : ?1=?2=?3μ1=μ2=μ3orB.)?0H0 : At least two of the group means ?1,?2,?3μ1,μ2,μ3 are not equal.2.) State the alternative hypothesis.A.) ??HA : At least two of the group means ?1,?2,?3μ1,μ2,μ3 are not equal orB.)??HA : ?1=?2=?3μ1=μ2=μ33.) What is the degrees of freedom for the denominator?A.) 12B.) 2C.) 3D.) 15 4.) What is the degrees of freedom for the numerator?A.) 2B.) 3C.) 12D.) 15

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.4: Discrete Random Variables; Applications To Decision Making

Problem 9E

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The following is sample information. We are asked to test the hypothesis at the 5% significance level that the treatment means are equal. Assume that the treatment results for each type of treatment are normally distributed with equal standard deviations (and variances).

Treatment I	Treatment II	Treatment III
9	13	10
7	20	9
11	14	15
9	13	14
12		15
10

1.) State the null hypothesis.

A.) ?0H0 : ?1=?2=?3μ1=μ2=μ3

B.)?0H0 : At least two of the group means ?1,?2,?3μ1,μ2,μ3 are not equal.

2.) State the alternative hypothesis.

A.) ??HA : At least two of the group means ?1,?2,?3μ1,μ2,μ3 are not equal

B.)??HA : ?1=?2=?3μ1=μ2=μ3

3.) What is the degrees of freedom for the denominator?

A.) 12

B.) 2

C.) 3

D.) 15

4.) What is the degrees of freedom for the numerator?

A.) 2

B.) 3

C.) 12

D.) 15

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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