Free Printable z-test & t-test

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z-test & t-test

Total questions: 20

Worksheet time: 28mins

Name

Class

Date

When should you use the t-test? (select all that apply)

When you are testing a proportion/percentage of a population

When you are testing for a mean

When you are given the population standard deviation

When you are ONLY given the sample standard deviation

Hypotheses must have a parameter or statistic such as $\overline{x},\ \mu,\ \sigma,\ s$

True

False

You do not need BOTH null and alternate hypotheses when testing

True

False

When testing with $\alpha=0.01$ you get $p=0.12$ . Your decision should be

Reject $H_0$ , there is a significant difference

Accept $H_0$ , there is NOT a significant difference

Reject $H_0$ , there is NOT a significant difference

Accept $H_0$ , there is a significant difference

When testing with $\alpha=0.05$ you get $p=3.2\ E^{-6}$ . Your decision should be

Reject $H_0$ , there is a significant difference

Accept $H_0$ , there is NOT a significant difference

Reject $H_0$ , there is NOT a significant difference

Accept $H_0$ , there is a significant difference

For the t-test one uses __________ instead of σ.

χ²

If you wish to test the claim that the mean of the population is 100, the appropriate alternate hypothesis is

$\overline{x}=100$

$\mu=100$

$\mu\ne100$

$\mu>100$

In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A random sample of 20 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At $\alpha=0.05$ , is the average height of the models really less than 67 inches? List test, p-value, and decision.

z-test, $p=0.002$ , Accept $H_0$

z-test, $p=7.98E^{-4}$ , Reject $H_0$

t-test, $p=0.003$ , Reject $H_0$

t-test, $p=0.005$ , Reject $H_0$

What is the only option for the null hypothesis?

H₀ = k

H₀ > k

H₀ < k

H₀ ≠ k

10.

The weight of the average 6th grade boy is 89 lbs. The principal of the school feeds them steak for first semester to see if their weight changes. What are the null and alternate hypotheses?

H₀: μ = 89

H₁: μ = 89

H₀: μ = 89

H₁: μ > 89

H₀: μ = 89

H₁: μ < 89

H₀: μ = 89

H₁: μ ≠ 89

11.

Find the critical value(s) for a two-tailed test with α = 0.05

z = -1.64

z = 1.64

z = ±0.06

z = ±1.96

12.

In a recent survey, the average amount of money

students have in their pockets is ₱280.80 with a standard

deviation of ₱62.40. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

₱289. What are the null and alternate hypotheses?

H₀: x̄ = ₱280.80

H₁: x̄ ≠ ₱280.80

H₀: x̄ = ₱280.80

H₁: x̄ > ₱280.80

H₀: x̄ = ₱280.80

H₁: x̄ < ₱280.80

H₀: x̄ > ₱280.80

H₁: x̄ = ₱280.80

13.

In a recent survey, the average amount of money

students have in their pockets is ₱120.40 with a standard

deviation of ₱57.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

₱254.50. Which test should be used?

z-test

t-test

z-test for proportion

χ²-test

14.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, what is the p-value for this test?

p = 0.456

p = 0.772

p = 0.228

p = 0.229

15.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, do we accept or reject the null hypothesis?

Accept H₀

Reject H₀

16.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, test the teacher’s claim that the

average amount of money is actually higher than $5.40.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim that the average amount of money is higher

There is not enough evidence to support the claim that the average amount of money is higher

17.

The average cost of a speeding ticket is $155. The population standard deviation is $10.78. A random sample of 35 speeding ticket court cases showed that the mean cost was $152.59. At the 0.05 significance level, is that less than $155?

Yes, there is a significant difference

Yes, there is not a significant difference

No, there is a significant difference

No, there is not a significant difference

18.

A P-value indicates:

the probability that the null hypothesis is true

the probability that the alternative hypothesis is true

the probability of obtaining the results (or one more extreme) if the null hypothesis is true

probability of a Type I error

19.

A car manufacturer advertises that its new subcompact models get an mean of 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated?

H₀ p= 47
H_a = 47

H₀ µ= 47
H_a < 47

Ha p= 47
H_a > 47

Ha µ= 47
H_a ≠ 47

20.

A real estate agent believes that the average closing cost of purchasing a new home is $6500. She selects 40 new home sales at random and finds that the average closing costs are $6600. The standard deviation of the population is $120. Test her belief at $\alpha=0.05$ . List test, p-value, and decision.

z-test, $p=1.36E^{-7}$ , Reject $H_0$

z-test, $p=6.81E^{-8}$ , Accept $H_0$

t-test, $p=5.32E^{-6}$ , Reject $H_0$

t-test, $p=2.66E^{-6}$ , Accept $H_0$

100 %

z-test & t-test

Total questions: 20

Worksheet time: 28mins

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