A school principal wants to know the average number of extracurricular activities students in her school are involved in. She assigned each student a number from 1 to 415. Using a random number generator, she selected 200 students to be part of the sample. She concluded that students are involved in an average of two extracurricular activities. Is the principal’s conclusion valid?(
The correct response is: Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.
While it is true that not all students in the sample may have extracurricular activities, that does not invalidate the principal's conclusion. The conclusion is based on the average number of activities of the students included in the sample, not whether every student in the sample participates in extracurricular activities.
The sample size of 200 is considered large enough for the Central Limit Theorem to apply, which allows for valid inferences about the population mean.
To determine whether the principal's conclusion is valid, we need to calculate the margin of error for the sample and compare it to the average number of activities.
The margin of error can be calculated using the formula:
Margin of error = (z-score) * (standard deviation / √n)
Since the population standard deviation is unknown, we can use the sample standard deviation as an estimate.
Let's assume that the standard deviation of the sample is 1.
Using a confidence level of 95%, the z-score for a 95% confidence interval is approximately 1.96.
Using the given values:
n = 200 (sample size)
standard deviation (estimate) = 1
z-score = 1.96
Plugging these values into the formula:
Margin of error = (1.96) * (1 / √200)
≈ 0.138
The margin of error is approximately 0.138.
Since the principal concluded that students are involved in an average of two extracurricular activities, and the margin of error is 0.138, we can say that the confidence interval for the average number of activities is (2 - 0.138, 2 + 0.138) or approximately (1.862, 2.138) with a confidence level of 95%.
Based on this analysis, we can conclude that the principal's statement of the average number of extracurricular activities is valid because the confidence interval includes the value of 2.
A school principal wants to know the average number of extracurricular activities students in her school are involved in. She assigned each student a number from 1 to 415. Using a random number generator, she selected 200 students to be part of the sample. She concluded that students are involved in an average of two extracurricular activities. Is the principal’s conclusion valid?(1 point)
Responses
Yes, because only those who have extracurricular activities were included in the sample.
Yes, because only those who have extracurricular activities were included in the sample.
No, because not all students in the sample have extracurricular activities.
No, because not all students in the sample have extracurricular activities.
Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.
Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.
No, because 200 students in the sample is too large.
A survey is conducted to determine the most common reason people own a cell phone. A company sent out a survey to customers between the ages of 20 and 30. Based on the responses, the company concluded that people own a cell phone for messaging purposes. Is this conclusion valid?(1 point)
Responses
No, because the sample includes customers of too many different ages.
No, because the sample includes customers of too many different ages.
Yes, because the sample includes male and female customers.
Yes, because the sample includes male and female customers.
Yes, because the sample includes all customers between the ages of 20 and 30.
Yes, because the sample includes all customers between the ages of 20 and 30.
No, because not all people who own a cell phone have the same probability of being selected.
The correct response is: No, because the sample includes customers of too many different ages.
The conclusion that people own a cell phone for messaging purposes cannot be valid if the sample includes customers of too many different ages. The age range for the survey was specified as between 20 and 30, so including customers outside of this age range introduces potential bias and makes it difficult to draw conclusions specifically about this age group.