Answer:
Null hypothesis:
![\mathtt{H_o : \mu = 21.21}](https://tex.z-dn.net/?f=%5Cmathtt%7BH_o%20%3A%20%5Cmu%20%3D%2021.21%7D)
Alternative hypothesis
t = -0.080
Decision Rule: To reject the null hypothesis if t > 1.340 at t
Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10
Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.
Step-by-step explanation:
Given that:
the sample mean
= 21.15
the standard deviation
= 4.7512
sample size N = 40
The objective is to test the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.
At the level of significance of 0.1
The null hypothesis and the alternative hypothesis for this study can be computed as follows:
Null hypothesis:
![\mathtt{H_o : \mu = 21.21}](https://tex.z-dn.net/?f=%5Cmathtt%7BH_o%20%3A%20%5Cmu%20%3D%2021.21%7D)
Alternative hypothesis
This test signifies a one-tailed test since the alternative is greater than or equal to 21.21
The t-test statistics can be computed by using the formula:
![t= \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%20%5Cdfrac%7B%5Coverline%20x%20-%20%5Cmu%20%20%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \dfrac{21.15- 21.21 }{\dfrac{4.7152}{\sqrt{40}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B21.15-%2021.21%20%20%7D%7B%5Cdfrac%7B4.7152%7D%7B%5Csqrt%7B40%7D%7D%7D)
![t = \dfrac{-0.06 }{\dfrac{4.7152}{6.3246}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B-0.06%20%20%7D%7B%5Cdfrac%7B4.7152%7D%7B6.3246%7D%7D)
t = -0.080
degree of freedom = n - 1
degree of freedom = 40 - 1
degree of freedom = 39
From the t statistical tables,
at the level of significance ∝ = 0.1 and degree of freedom df = 39, the critical value of ![\mathtt{{T_{39,0.10} = 1.304}}](https://tex.z-dn.net/?f=%5Cmathtt%7B%7BT_%7B39%2C0.10%7D%20%3D%201.304%7D%7D)
Decision Rule: To reject the null hypothesis if t > 1.340 at t
Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10
Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.