Question

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.

Answer 1

Following are the responses to the given question:

Explanation:

Follows are the description of the null and alternative Hypothesis:

`H_0: \mu = 148.4\\\\H_a: \mu \\eq 148.4`

Region of rejection

`\alpha = 0.01\\\\ df = 49\\\\`

Calculating the critical value:

`t = \pm 2.68 \\\\H_0\ when\ t < -2.68 \ or\ t > 2.68`

Testing statistic values:

`t = \frac{(\bar{x} - \mu)}{((s)/(√(n)))}`

`= ((147.8 - 148.4))/(((2.3)/(√(50))))\\\\ = (-0.6)/(((2.3)/(7.07)))\\\\= (-0.6)/(0.325)\\\\ = -1.846`

`P-value = 0.0711`

`P-value \geq 0.01,` fail to reject null hypothesis.

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