Data below corresponds to sample weights of two different types (A and B) of Tuna.

We want to test at significance level � = .05 if the two tuna populations from which
the samples come have the same variance.
A .99 1.92 1.23 .85 .65 .69 .6 .53 1.41 1.12 .63 .67 .6 .66 1.9
B 2.56 1.92 1.3 1.79 1.23 .62 .66 .62 .65 .6 .67
Figure 1: Tuna weights
[5] (a) Compute sample variances S2
1 and S2
2 of the two types A and B.
[5] (b) Run the appropriate statistical test and conclude if there is a difference in the
two population variances.

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

However, I will give you a start.

Find the means first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

I'll let you do the calculations and choose the statistical test.

To compute the sample variances for the two types of tuna, we can use the formula for sample variance:

Sample Variance (S^2) = ((Σ(Xi - X̄)^2) / (n - 1))

where:
- Σ indicates the sum of
- Xi represents each individual data point
- X̄ is the mean of the data set
- n is the sample size

For type A:

1. Calculate the mean of type A Tuna weights:
X̄ = (Sum of all type A data points) / (Number of type A data points)
= (0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.69 + 0.6 + 0.53 + 1.41 + 1.12 + 0.63 + 0.67 + 0.6 + 0.66 + 1.9) / 15
= 15.84 / 15
= 1.056

2. Substitute the values into the formula for sample variance:
S^2_1 = ((Σ(Xi - X̄)^2) / (n - 1))
= ((1.056 - 0.99)^2 + (1.056 - 1.92)^2 + (1.056 - 1.23)^2 + ... + (1.056 - 1.9)^2) / (15 -1)

Calculate the sum of squares of the differences from the mean:
Sum of squares = ((1.056 - 0.99)^2 + (1.056 - 1.92)^2 + (1.056 - 1.23)^2 + ... + (1.056 - 1.9)^2)
= (0.066)^2 + (-0.864)^2 + (-0.174)^2 + ... + (-0.844)^2

Then, divide the sum of squares by (n - 1) to find the sample variance (S^2_1).

Repeat the same process for type B to compute S^2_2.

(b) To test if there is a difference in the two population variances, we can use the F-test. The F-test compares the ratio of variances between two samples to a known F-distribution.

The null hypothesis is that the two populations have equal variances, and the alternative hypothesis is that the variances are different.

Calculate the test statistic F:
F = (S^2_1) / (S^2_2)

In this case, we will compare F with the critical F-value at the given significance level (α = 0.05). The critical F-value can be found using statistical tables or calculators.

If the calculated F-value is greater than the critical F-value, we reject the null hypothesis and conclude that the two populations have different variances. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in variances.