Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are

nequals=197197​,

x overbarxequals=5.845.84​,

sequals=1.921.92.

Use a

0.010.01

significance level to test the claim that the population mean of such ratings is less than

6.006.00.

Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

muμequals=6.006.00

Upper H 1H1​:

muμnot equals≠6.006.00

B.

Upper H 0H0​:

muμequals=6.006.00

Upper H 1H1​:

muμless than<6.006.00

C.

Upper H 0H0​:

muμequals=6.006.00

Upper H 1H1​:

muμgreater than>6.006.00

D.

Upper H 0H0​:

muμless than<6.006.00

Upper H 1H1​:

muμgreater than>6.006.00

Determine the test statistic.

nothing

​(Round to two decimal places as​ needed.)

Determine the​ P-value.

nothing

​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

▼

Upper H 0H0.

There is

▼

evidence to conclude that the mean of the population of ratings is

▼

6.006.00.

Answer 1

H0: >= 6

Ha: < 6

Test statistics

t = - / S / sqrt(n)

= 5.84 - 6 / 1.92 / sqrt(197)

= -1.17

From T table,

Using test statistics -1.17 and df of 196 ,

p-value = 0.122

Since p-value > 0.01, we fail to reject H0.

We conclude at 0.01 level that

There is insufficient evidence to conclude that the mean of the population of rating is less than 6