A column is going from top to bottom
Answer:
x = 4
Step-by-step explanation:
First u need to distribute the -1 to (x + 4), creating the equation, -8 = -x - 4. Then add the -4 to both sides, and you get, -4 = -x. Then divide by -1 to both sides, and x = 4.
Answer:
a) ![[-0.134,0.034]](https://tex.z-dn.net/?f=%5B-0.134%2C0.034%5D)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where
.
The mean difference
.
The confidence interval is
![(\mu_1 - \mu_2) \pm t_{n_1+n_2-2,\alpha/2} \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}} = (-0.05) \pm t_{68,0.025} \sqrt{\frac{0.03}{40} + \frac{0.03}{30}}](https://tex.z-dn.net/?f=%28%5Cmu_1%20-%20%5Cmu_2%29%20%5Cpm%20t_%7Bn_1%2Bn_2-2%2C%5Calpha%2F2%7D%20%5Csqrt%7B%5Cfrac%7Bs_p%5E2%7D%7Bn_1%7D%20%2B%20%5Cfrac%7Bs_p%5E2%7D%7Bn_2%7D%7D%20%3D%20%28-0.05%29%20%5Cpm%20t_%7B68%2C0.025%7D%20%5Csqrt%7B%5Cfrac%7B0.03%7D%7B40%7D%20%2B%20%5Cfrac%7B0.03%7D%7B30%7D%7D)
![= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]](https://tex.z-dn.net/?f=%3D%20-0.05%5Cpm%201.995%20%5Ctimes%200.042%20%3D%20-0.05%20%5Cpm%200.084%20%3D%20%5B-0.134%2C0.034%5D)
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.