Respuesta :
Answer:
A) The test statistic is approximately 7.5056
B) E. There is no evidence that diet is independent of backfat thickness
Step-by-step explanation:
The given data are;
The sample mean for pigs raised on Diet 1, [tex]\overline x_1[/tex] = 3.63 cm
The sample SD for pigs raised on Diet 1, s₁ = 0.29 cm
The number of pigs in the sample for pigs raised on Diet 1, n₁ = 18
The sample mean for pigs raised on Diet 2, [tex]\overline x_2[/tex] = 3.37 m
The sample SD for pigs raised on Diet 2, s₂ = 0.25 cm
The number of pigs in the sample for pigs raised on Diet 2, n₂ = 18
The pooled SE = 0.09
A) The test statistic is given by the following formula;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(3.63-3.37)}{\sqrt{\dfrac{0.29^{2} }{18}-\dfrac{0.25^{2}}{18}}} \approx 7.5056[/tex]
The test statistic, t ≈ 7.5056
B) The degrees of freedom, df = n₁ - 1 = 18 - 1 = 17
At a confidence level of 95%, the critical value is 2.11
Given that the value of the test statistics tic if larger than the critical value, the null hypothesis is rejected and there is a difference in the backfat of the pigs on different diet
Therefore, there is no evidence that diet is independent of backfat thickness
