Respuesta :
Answer:
d) The difference exists due to chance since the test statistic is small
Step-by-step explanation:
From the given information:
Population mean = 178 cm
the sample mean = 177.5 cm
the standard deviation = 2
the sample size = 25
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis:
[tex]H_o: \mu = 178[/tex]
Alternative hypothesis:
[tex]H_1: \mu \neq 178[/tex]
The t-test statistics is determined by using the formula:
[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}[/tex]
[tex]t = \dfrac{-0.5}{\dfrac{2}{5}}}[/tex]
[tex]\mathbf{t= -1.25}[/tex]
Degree of freedom df = n- 1
Degree of freedom df = 25 - 1
Degree of freedom df = 24
At the level of significance ∝ = 0.05, the critical value = 2.064
Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance
Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small
Answer:
d. The difference exists due to chance since the test statistic is small
Step-by-step explanation:
With a very small sample size of 25, a difference of 0.5 cm is most likely due to chance.
