The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?
Yes, because the computed t lies in the rejection region.
No, because the information given is not complete.
No, because the computed t lies in the area to the right of -2.718.
Yes, because 43 is greater than 41.5.

The correct option is;

Yes because the computed t lies in the rejection region

Step-by-step explanation:

Here we have

The calculated mean of the values given as

= Sample mean = 41.5

μ = Population mean = 43

σ = Standard deviation 1.784

The confidence interval is

At 0.02 the critical t is 2.718 with a p value of 0.014 which is less than the confidence level at 0.02. We therefore reject the null hypothesis and we fail to reject the alternate hypothesis which states that there has been a change in the mean length

Therefore the answer is Yes because the computed t lies in the rejection region.

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt