James has a desk job and would like to become more fit, so he purchases a tread walker and a standing desk which will allow him

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1 month ago

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James has a desk job and would like to become more fit, so he purchases a tread walker and a standing desk which will allow him

to walk at a slow pace as he works. However, he is concerned that standing and walking while working may cause his productivity to decline. After working this way for 6 months he takes a simple random sample of 15 days. He records how long he walked that day (in hours) as recorded by his fitness watch as well as his billable hours for that day as recorded by a work app on his computer. Assuming that all conditions for inference are met, which of the following is a 95 percent confidence interval for the average change in the number of billable hours for each increase of 1 hour spent walking?

Mathematics

2 answers:

Inessa [12.5K] · Answer 1 · 2026-02-26T18:56:28+03:00

Answer:

The answer is

$-0.245 \pm2.160(0.205)$

Step-by-step explanation:

After operating under these conditions for a period of 6 months, he selects a simple random sample of 15 days. He logs the hours he walked each day as tracked by his fitness monitor, alongside his recorded billable hours from a work application on his computer.

The calculated slope is -0.245

The number of samples is n = 15

The standard error is 0.205

The confidence level is 95

The significance level is (100 - 95)% = 0.05

The degrees of freedom is n - 2 = 15 - 2 = 13

Critical Value = 2.16 = [using excel = TINV (0.05, 13)]

Marginal Error = Critical Value * standard error

= 2.16 * 0.205

= 0.4428

$-0.245 \pm2.160(0.205)$

lawyer [12.5K] · Answer 2 · 2026-02-26T18:59:00+03:00

Answer:

The right answer is C. [-0.245±2.160*0.205]

Step-by-step explanation:

Greetings!

To evaluate whether walking during work (independent variable X) influences his work efficiency (dependent variable Y), James considered a random sample of 15 days from a 6-month duration of working and training at home, noting how long he walked and his billable hours for each respective day.

From this data, he calculated the linear regression relating work productivity to the time allocated for walking.

^Y= 7.785 -0.245X

The goal is to determine how the mean number of billable hours changes with each additional hour spent walking.

To find the range of potential values for the average billable hours with each hour increase in walking time, it's necessary to compute a confidence interval for the population slope in the regression. The statistic is assessed using a t-test:

$t= \frac{b-\beta}{Sb} ~~t_{n-1}$

[b± $t_{n-2;1-\alpha /2}$ *Sb]

Utilizing a 95% confidence level, the t value is $t_{n-2;1-\alpha /2}= t_{13; 0.975}= 2.160$

b= -0.245

Sb= 0.205

[-0.245±2.160*0.205]

[-0.68780.1978]

With a confidence level of 95%, the interval [-0.68780.1978] is expected to include the average billable hours when walking time is increased by 1 hour.

I trust this is helpful!