Question

Researchers did a study to compare how much people in their teens (13–19 years old) and twenties (20–29 years old) talk in a day. It is commonly thought that teenagers talk more than older people. The study collected data from a simple random sample of teenagers and a simple random sample of people in their twenties. For each individual in these samples the researchers gave the estimated number of words spoken in a day. The data is in the accompanying file. (a) (4 points) Do the data provide good evidence that teenagers talk more than people in their twenties, on average? State the null and alternative hypotheses relative to this question. (B) what is test statcis , P value and conclusions.

This X bar 1=1496.11111 Standard Deviation 1=7914.34522 N=27

Second X bar= 12866.7 Standard De:8342.472183 N=20

Answer 1

Assumptions :

Data come from normal distribution.

Population variances are equal.

a) Claim : On average, teenagers talk more than people in their twenties.

The hypothesis are :

H0 :
11 = 2
v/s H1:
271 <17

b) The test statistic is,

1- 72. t=- s* V +

where,

(n1- 1) + S +(n2 - 1) + số nl + n2 - 2

(27-1) * 7914.345222 + (20 -1)*8342.4721832 274 20-2

= 8097.87128

The test statistic value is,

1496.11111 - 12866.7 t= 8097.87128

= -4.759

df = 27 + 20 -2 = 45

p value = p ( t > -4.759 )

= 0.9999 -----------( using excel formula "=t.dist.rt( -4.759,45) " )

Here p value > $\alpha$ ( 0.05)

Hence we failed to reject null hypothesis.

Conclusion : There is no sufficient evidence to support the claim that teenagers talk more than people in their twenties.