State the Type I and Type II errors in complete sentences given the following statements.

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

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

f. The mean number of cars a person owns in his or her lifetime is not more than ten.

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

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities mean tuition cost is more than \)20,000 per year.

The one-sample t-test is a statistical hypothesis test that is used to evaluate if an unknown population mean differs from a given value.

Rejecting the null hypothesis $H_0$when it is true is defined as a $TypeI$error:

If the $H_0$is: "The mean number of years Americans work before retiring is $34$," than $TypeI$error is

• One thinks the mean is not $34$years when, in fact, it really is $34$years.
• $TypeII$error is One thinks the mean is $34$years when, in fact, it really is not $34$years.

Type I error: We conclude that more than $60\%$Americans vote in presidential elections when the actual percentage is at most $60\%$.

Type II error: We conclude that most $60\%$Americans vote in presidential elections when, in fact, more than $60\%$do.

$TypeI$error: One thinks the mean starting salary is less than $100,000$, in fact, it really is at least $100,000$

$TypeII$error: We conclude that the mean starting salary is at least $100,000$when, in fact, it really is less than $100,000$

$TypeI$error: We conclude that the proportion of high school seniors who get drunk each month is not $29\%$, when it really is $29\%$.

$TypeII$ error: We conclude that the proportion of high school seniors who get drunk each month is $29\%$when, in fact, it is not $29\%$

$TypeI$error: One thinks fewer than $5\%$adults ride the bus to work in Los Angeles when the percentage that does is real $5\%$or more.

$TypeII$error: One thinks more adults $5\%$ride bus tow work.

$TypeI$error: One thinks 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 $10$.

$TypeII$error: One thinks the mean number of cars a person owns in his or her lifetime is not more than $10$when, in fact, it really is more than $10$.

$TypeI$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.

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

$TypeI$error: We conclude that the duration of paid vacations each year for Europeans is not six weeks when it really is six weeks.

$TypeII$error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it really is not.

$TypeI$ error: One thinks the proportion is less than $11\%$when it is really at least $11\%$.

$TypeII$ error: One thinks the proportion of women who develop breast cancer is at least $11\%$when it is really less than $11\%$.

$TypeI$error: One thinks the average tuition cost at private universities is more than $20,000$, though in reality, it is at most $20,000$

$TypeII$error: One thinks that the average tuition cost at private universities is at most $20,000$when, in fact, it is more than $20,000$

The final result state that, Type $I$and Type $II$errors in complete sentences given statements.