A researcher was interested about the weekly average usage of a local park in San Antonia, Texas. A study was designed to study the relationship between age and number of times residents visited the park each week. They were interested to see if age tends to impact the number of times residents visit the park. The surveyor collected responses information about age and the number of visits per week from 118 residents of San Antonia, Texas. They provided them with an anonymous paper survey to fill out. Required:
a. What are the observational units in this study?
b. Is number of visits per week the explanatory or response variable?
c. Is age the explanatory or response variable?
d. Is this an observational study or a randomized experiment?
e. What is the most concerning type of bias in this study? Why?
f. What is the appropriate scope of inference in this study

a) Residents of San Antonia, Texas

b) Response variable

c) Explanatory variable

d) Observational study

e) Response bias

f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"

Step-by-step explanation:

a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.

b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.

c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.

d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.

e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.

f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

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step-by-step explanation:

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