Question

The local library if they get more patrons visiting by shifting some early morning hours to evening. They take a sample of days with morning hours included 8-5pm compared to 12-9pm.

8am-5pm hours: 50, 40, 60, 60, 70, 35, 40

12-9 PM hours : 40, 80, 70, 60, 85, 90, 70

1. Provide null and alternative hypotheses in formal terms and layperson's terms for the t test for independent samples

2. Do the math and reject or accept at a=.05

3. Explain the results in layperson's terms

4. Calculate and explain a 95% confidence interval in layperson's terms if appropriate.

The library thinks the average number of patrons for 12-9 PM hours is 60. Use the data for 12-9 from the previous question

1. Provide the null and alternative hypotheses formal and layperson’s informal terms for a t one-sample test.

2. Do the math and reject or accept at a=0.05

3. Explain the results in layperson’s terms

Answer 1

(1)

H0: Null Hypothesis: (More patrons do not visit   evening than early morning)

HA: Alternative Hypothesis: ( More patrons visit   evening than early morning) (claim)

(2)

n1 = 7

1 = 50.7143

s1 = 13.0475

n2 = 7

2 = 70.7143

s2 = 16.9383

Test Statistic is given by:

t = (50.7143 - 70.7143)/8.0812

= - 2.4749

= 0.05

ndf = n1 + n2 - 2 = 7 + 7 - 2 = 12

From Table, critical value of t = - 1.7823

Since calculated value of t = - 2.4749 is less than critical value of t = -1.7823:

Reject null hypothesis.

(3)

Data support the claim that more patrons visit   evening than early morning.

(4)

From Table, critical values of t = 2.1788

Confidence Interval:
(50.7143 - 70.7143) (2.1788 X 8.0812)

- 20 17.6073

= ( - 37.6073 , - 2.3927)

(5)

H0: Null Hypothesis: ( the average number of patrons for 12-9 PM hours is 60.) (claim)

HA: Alternative Hypothesis: ( the average number of patrons for 12-9 PM hours is not 60.)

(2)

SE = s/

= 16.9383/

= 6.4021

Test Statistic is given by:

t = (70.7143 - 60)/6.4021

= 1.67

ndf = 7 - 1 = 6

= 0.05

From Table, critical values of t = 2.4469

Since calculated value of t is less than critical value of t, Fail to reject H0.

(3)

The data support the claim that the average number of patrons for 12-9 PM hours is 60.