Historically, the average time it takes KIm to swim the 200 meter butterfly is 148.4 seconds. Kim would like to know if her average time has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 with a standard deviation of 2.3 seconds. Determine the null and alternative hypothesis, and your conclusion at the level of significance .01.

Following are the responses to the given question:

Step-by-step explanation:

Follows are the description of the null and alternative Hypothesis:

Region of rejection

Calculating the critical value:

Testing statistic values:

fail to reject null hypothesis.

There are just not enough evidence of increases in surface times.

i need the options

step-by-step explanation:

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