Question

Identifying Signs For the sign test described in Exercise 1, identify the number of positive signs, the number of negative signs, the number of ties, the sample size n that is used for the sign test, and the value of the test statistic.

Short answer

• The number of positive signs is equal to 2.
• The number of negative signs is equal to 7.
• The number of ties is equal to 1.
• The sample size is equal to 10.
• The value of the test statistic is equal to 2.

Step-by-step solution

Given information

Two samples are given showing the weights of students (kgs) in September and April.

Describe the sign test

The sign test is a type of non-parametric test that can is used to test the claim of no difference in the values of the weights between September and April.

The table of weights of the two samples is given below.

September weight (kg)	67	53	64	74	67	70	55	74	62	57
April weight (kg)	66	52	68	77	67	71	60	82	65	58

Explain the sign of difference

If the value of the September weight is greater than that of the April weight, the sign of difference is positive.

If the value of the September weight is less than that of the April weight, the sign of difference is negative.

If the value of the September weight is equal to that of the April weight, the difference is zero.

The signs of the differences between September weights and April weights are shown below.

September weight (kg)	67	53	64	74	67	70	55	74	62	57
April weight (kg)	66	52	68	77	67	71	60	82	65	58
Sign of difference	+	+	-	-	0	-	-	-	-	-

The number of positive signs is equal to 2.

The number of negative signs is equal to 7.

The number of ties (equal values of weights) is equal to 1.

Find the sample size

The number of observations in each sample is equal to 10.

Therefore, the sample size (n) is equal to 10.

Find the test statistic

As n is less than 25, the test statistic is denoted by x, and it is the number of times the less frequent sign occurs.

Here, the less frequent sign is the positive sign.

The number of times the positive sign occurs is equal to 2.

Thus, the value of the test statistic is equal to 2.