When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:
a n ⋅ b n = (a ⋅ b) n
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
When the bases and the exponents are different we have to calculate each exponent and then multiply:
a n ⋅ b m
Example:
32 ⋅ 43 = 9 ⋅ 64 = 576
<em>b</em><em> </em>for <em>books</em><em> </em>read. b=1x + 1. the amount of months he's been in the club goes for x and +1 because he already read a book before he joined. if you do easy math, he's been there for 8 months because he read 9 books. i probably got the equation backwards but this works both ways imo.
a. The standard error is equal to the standard deviation divided by the square root of the sample size:
SE = (23 ppm)/√18 ≈ 5.42 ppm
b. The t statistic is given by the difference between the true and sample means, divided by the standard error:
t = (192 ppm - 180 ppm)/SE ≈ 2.21
c. The p-value is approximately 0.0204.
d. Since p < 0.05, the difference is significantly different, so we reject the null hypothesis.
e. A type I error might have occurred, since it's possible that the null hypothesis was true, but we ended up rejecting it.
