Ages of mothers at first birth were recorded for a random sample of 14 mothers in England. A sign test is to be used to test the hypothesis that the median age of mothers at first birth is 30. It is found that the number of values lying below the assumed value for the population median is 3 and the number of values lying above the assumed median is 11.

The following table gives the probability distribution for a random sample of size 14.

Number of [+]s, x	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
P(x[+])	0.000	0.001	0.006	0.022	0.061	0.122	0.183	0.209	0.183	0.122	0.061	0.022	0.006	0.001	0.000

Use the table to calculate the p-value for this hypothesis test. Hence select the answer that gives the correct conclusion for this test.

For convenience, Unit 6 Table 10 (Subsection 5.1) is reproduced here.

p value	Rough interpretation
p > 0.10	Little evidence against the hypothesis
0.10p> 0.05	Weak evidence against the hypothesis
0.05p> 0.01	Moderate evidence against the hypothesis
0.01p > 0.001	Strong evidence against the hypothesis
0.001p	Very strong evidence against the hypothesis

Select one:

There is little evidence against the hypothesis.

There is strong evidence against the hypothesis.

There is weak evidence against the hypothesis.

There is moderate evidence against the hypothesis.

There is very strong evidence against the hypothesis.