Question

In: Statistics and Probability

Three groups of guinea pigs were injected respectively with 0.5mg, 1.0mg and 1.5mg of a tranquillizer,...

Three groups of guinea pigs were injected respectively with 0.5mg, 1.0mg and 1.5mg of a tranquillizer, and the following are the number of seconds it took them to fall asleep:

0.5mg 8.2 10 10.2 13.7 14 7.8 12.7 10.9 10.9 10.4 1.0mg 9.7 13.1 11 7.5 13.3 8.8 12.5 12.9 9.7 10.5 1.5mg 12 7.2 8 9.4 11.3 9 11.5 8.5 9.6 9.2

It is required to use the data to test whether differences in dosage have effect on the length of time it takes guinea pigs to fall asleep.

Assuming that the reduction in cholesterol level by the drugs are continuous with same shape and variability, answer questions 1 to 3.

1. Compute the test statistic for the most appropriate test correct to 4 significant figures.

2. Compute the corresponding significance probability correct to four decimal places

3. Suppose a follow-up pairwise comparison tests are being conducted at 10% significance level, what will be the value of the least significance difference(LSD) correct to 2 decimal places.

Expert Solution

Answer:-

Given That:-

Three groups of guinea pigs were injected respectively with 0.5mg, 1.0mg and 1.5mg of a tranquillizer, and the following are the number of seconds it took them to fall asleep

1. Compute the test statistic for the most appropriate test correct to 4 significant figures.

Given,

The F - test statistics for the most appropriate test is,

By uisng Excel software, find F - test ststistics with the help of following steps:

1) Import the data

2) Choose ANOVA: Single Factor from Data Analysis in Data menu.

3) Choose Input Range and Column in Groups by.

4) Choose Output Range.

5) Click ok

From the excel output, the F - test statistics for the most appropriate test is 1.6061.

2. Compute the corresponding significance probability correct to four decimal places

The corresponding significant probability (p-value) is,

From Excel output in part(1), the corresponding significant probability (p-value) is 0.2193

3. Suppose a follow-up pairwise comparison tests are being conducted at 10% significance level, what will be the value of the least significance difference(LSD) correct to 2 decimal places.

The Fisher's LSD value is,

First, compute t critical value then find Fisher's LSD value.

The t critical value is,

The sample size is small and two - tailed test. look in the column headed and the row headed in the t distribution table by using degree of freedom within is 27 and the t critical value is 1.703.

The critical value of Fisher's LSD is,

= 1.45

The critical value of Fisher's LSD is 1.45

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orchestra answered 1 year ago

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