A company advertises that its cans of caviar each contain 100 g of their product. A consumer advocacy group doubts this claim, and they obtain a random sample of 8 cans to test if the mean weight is significantly lower than 100 g. They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. The advocacy group wants to use these sample data to conduct a t-test on the mean. Assume that all conditions for inference have been met. Provide the correct test statistic formula for their significance test.

The value of the test statistic is -3.14.

Step-by-step explanation:

Test statistic:

In which X is the sample mean, is the expected value, is the standard deviation and n is the size of the sample.

A company advertises that its cans of caviar each contain 100 g of their product.

This means that

They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. Sample of 8 cans.

This means that

So the test statistic will be given by:

The value of the test statistic is -3.14.

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

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