Question

The mean weight of males aged over 30 years in a certain population is 76 KG. Recently there was some tendency among this population to practice exercises to reduce weight. A random sample of size 40 is selected and it is found that sample mean and standard deviation are 74 and 8 respectively. Do the data provide sufficient evidence to conclude that the mean weight for this population has reduced. Use 5% significance level.

please can someone help

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses are as follows :

Test statistic :

To test the hypothesis the most appropriate test is one sample t-test. The test statistic is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and μ is hypothesized value of population mean under H_{​​​​​​0}.

Where, x̅ = 74 kg,  μ = 76 kg, s = 8 kg and n = 40

The value of the test statistic is -1.5811.

P-value :

Since, our test is left-tailed test, therefore we shall obtain left-tailed p-value for the test statistic. The left-tailed p-value is given as follows :

P-value = P(T < t)

P-value = P(T < -1.5811)

P-value = 0.0610

The p-value is 0.0610.

Decision :

Significance level = 5% = 0.05 and p-value = 0.0610

(0.0610 > 0.05)

Since, p-value is greater than the significance level of 5%, therefore we shall be fail to reject the null hypothesis (H_{​​​​​​0}) at 5% significance level.

Conclusion :

At 5% significance level, there is not sufficient evidence to conclude that the mean weight for the population has reduced.

Please rate the answer. Thank you.