Question

In: Statistics and Probability

a). Consider the following. Fewer than 5% of adults in Los Angeles ride the bus to...

a). Consider the following.

Fewer than 5% of adults in Los Angeles ride the bus to work.

State the Type I and Type II errors in complete sentences.

Type I error: We believe that at least 5% of adults in Los Angeles ride the bus to work when the percentage really is fewer than 5%.
Type II error: We believe that fewer than 5% of adults in Los Angeles ride the bus to work when the percentage really is greater than or equal to 5%. Type I error: We believe that fewer than 5% of adults in Los Angeles ride the bus to work when the percentage really is greater than or equal to 5%.
Type II error: We believe that at least 5% of adults in Los Angeles ride the bus to work when the percentage really is fewer than 5%.      Type I error: We believe that the percentage of adults in Los Angeles who ride the bus to work is 5% when it really is not 5%.
Type II error: We believe that the percentage of adults in Los Angeles who ride the bus to work is not 5% when it really is 5%. Type I error: We believe that the percentage of adults in Los Angeles who ride the bus to work is not 5% when it really is 5%.
Type II error: We believe that the percentage of adults in Los Angeles who ride the bus to work is 5% when it really is not 5%.

b). Consider the following.

The average number of cars a person owns in his or her lifetime is not more than 10.

State the Type I and Type II errors in complete sentences.

Type I error: We believe that the average number of cars a person owns in his or her lifetime is 10 when it really is not 10.
Type II error: We believe that the average number of cars a person owns in his or her lifetime is not 10 when it really is 10. Type I error: We believe that the average number of cars a person owns in his or her lifetime is more than 10 when it really is not more than 10.
Type II error: We believe that the average number of cars a person owns in his or her lifetime is not more than 10 when it really is more than 10.      Type I error: We believe that the average number of cars a person owns in his or her lifetime is not more than 10 when it really is more than 10.
Type II error: We believe that the average number of cars a person owns in his or her lifetime is more than 10 when it really is not more than 10. Type I error: We believe that the average number of cars a person owns in his or her lifetime is not 10 when it really is 10.
Type II error: We believe that the average number of cars a person owns in his or her lifetime is 10 when it really is not 10.

c). Consider the following.

About half of Americans prefer to live away from cities, given the choice.

State the Type I and Type II errors in complete sentences.

Type I error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is less than 50% when it really is more than 50%.
Type II error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is more than 50% when it really is less than 50%.Type I error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is more than 50% when it really is less than 50%.
Type II error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is less than 50% when it really is more than 50%.     Type I error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is not around 50% when it really is around 50%.
Type II error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is around 50% when it really is not around 50%.Type I error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is around 50% when it really is not around 50%.
Type II error: We believe that the percentage of Americans who, given the choice, prefer to live away from cities is not around 50% when it really is around 50%.

Solutions

Expert Solution

Q1)
Type I error: We conclude that fewer than 5% of adults Angeles, when the percentage that do is really 5% or more.
Type II error: We conclude
that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that
5% do

Q2)

Type I error: We conclude that the mean number of cars a person owns in his or her
lifetime is more than 10, when in reality it is not more than 10.

Type II error: We
conclude that the mean number of cars a person owns in his or her lifetime is not
more than 10 when, in fact, it is more than 10

Q3)

Type I error: We conclude that the proportion of Americans who prefer to live away
from cities is not about half, though the actual proportion is about half.

Type II error:
We conclude that the proportion of Americans who prefer to live away from cities is
half when, in fact, it is not half.

orchestra answered 2 years ago
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