Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
(a) Construct and interpret a 90% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

Step-by-step explanation:

Data provided

represent the sample mean for the steps

population mean

s=2313 represent the sample standard deviation

n=61 represent the sample size  

Solution

The confidence interval for the true population mean is given by :

  (1)

Since we need to find the critical value we need to calculate first the degrees of freedom, given by:

The Confidence is 0.90 or 90%, the value for the significance is and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that

Now we have everything in order to replace into formula (1):

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

it is 570

step-by-step explanation: