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The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. to investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. to do so, 40 volunteers are recruited. half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. the other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. the volunteers are monitored for 30 days. the mean and standard deviation of the number of steps taken per day are computed for each group. here are the data:

Respuesta :

The confidence interval for the difference in the mean number of steps is; 1596 ± 2.861√[(1580²/20) + (2350²/20)]

What is the confidence Interval?

The given data is;

                                          n                      x⁻                   Sₓ

Pay attention                    20                 10,244            1,580

Do not pay attention        20                 8.,648            2,350

We are given;

Significance level; α = 0.1

Using Excel with the function, we have: TINV(0.01,19);

Critical value is; t = 2.861

The margin of error can now be represented by the illustration:

Margin of error = t√[(s₁²/n₁) + (s₂²/n₂)]

Thus, the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:

1596 ± 2.861√[(1580²/20) + (2350²/20)]

Read more about Confidence Interval at; https://brainly.com/question/17097944

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