Data were collected on the differences in weight gains of 12 people one
month after they stopped smoking, compared with their weight at the time
when they stopped smoking. The data are given in Table 2. A positive
quantity corresponds to a gain in weight, a negative quantity to a loss.
Table 2
Person no 1 - weight difference =1.0
person no 1 - weight difference= 2.3
Person no 3 - weight difference= -0.8
person no 4 - weight difference=0.1
person no 5 - weight difference=2.0
person no 6 - weight difference=0.9
person no 7 - weight difference=-0.3
person no 8 - weight difference=2.4
person no 9 - weight difference=-0.5
person no 10 - weight difference=2.5
person no 11 - weight difference=-1.3
person no 12 - weight difference= 2.1
A sign test is to be performed to investigate whether or not people gain
weight after stopping smoking.
(a) Write down the hypothesis to be tested. [1]
(b) Record the number of values lying above and the number lying below
the hypothesised value. What is the value of the test statistic? [2]
(c) What is the appropriate critical value at the 5% significance level? [1]
(d) Decide whether or not you would reject the hypothesis at the
5% significance level. [1]
please help me i need to have an answer to this its the deadline today
To perform a sign test to investigate whether people gain weight after stopping smoking, we need to follow these steps:
(a) Write down the hypothesis to be tested:
In this case, the null hypothesis would be that people do not gain weight after stopping smoking, while the alternative hypothesis would be that people do gain weight after stopping smoking.
H0: People do not gain weight after stopping smoking
H1: People gain weight after stopping smoking
(b) Record the number of values lying above and below the hypothesized value:
We need to count the number of values that are positive (indicating weight gain) and the number of values that are negative (indicating weight loss) in the given data.
In this case, we have:
Number of positive values: 7 (counting weight gains)
Number of negative values: 5 (counting weight losses)
The test statistic is the smaller of the two counts, so in this case, the test statistic is 5.
(c) Find the appropriate critical value at the 5% significance level:
To find the critical value, we can use a sign test table or a binomial distribution table. For a two-tailed test at the 5% significance level, we divide the significance level by 2 to get 0.025. Looking up the critical value for n=12 and p=0.5 (assuming the null hypothesis is true), we find that the critical value is 3.
(d) Decide whether to reject the hypothesis at the 5% significance level:
To decide whether to reject the null hypothesis, we compare the test statistic to the critical value. If the test statistic is less than or equal to the critical value, we reject the null hypothesis; otherwise, we fail to reject it.
In this case, the test statistic is 5, which is greater than the critical value of 3. Therefore, we fail to reject the null hypothesis at the 5% significance level.
In conclusion, based on the sign test performed, there is not enough evidence to suggest that people gain weight after stopping smoking.