Final answer:
To subtract 4.0 × 10⁻⁷ from 5.0 × 10⁻⁶, first convert 5.0 × 10⁻⁶ to the same exponent level, resulting in 50.0 × 10⁻⁷. Then subtract the numbers to get 46.0 × 10⁻⁷, which is written in scientific notation as 4.6 × 10⁻⁶.
Step-by-step explanation:
To subtract 4.0 × 10⁻⁷ from 5.0 × 10⁻⁶, you need to express both numbers with the same exponent. Convert 5.0 × 10⁻⁶ to a number with an exponent of ⁻⁷ by moving the decimal place one position to the left, yielding 50.0 × 10⁻⁷. Now you can directly subtract the normal parts (i.e., the coefficients in front of the powers of ten):
50.0 × 10⁻⁷ - 4.0 × 10⁻⁷ = 46.0 × 10⁻⁷
Finally, the result can be written in scientific notation as 4.6 × 10⁻⁶ by moving the decimal one place to the right to match the original exponent in the problem.
One null hypothesis that can be analyzed by a chi-squared test is whether the distribution of two populations is the same, even if the specific distribution is unknown. This is referred to as the test for homogeneity.
The null hypothesis asserts that the populations of the two data sets come from the same distribution. The test compares the observed values against the expected values if the populations followed the same distribution.