A random sample of 25 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.54 mm and sample standard deviation is S = 0.20 mm. Construct a 95% two-sided confidence interval for the mean glass thickness.

Answer: (3.46, 3.62)Step-by-step explanation:The formula to find the confidence interval for population mean is given :-[tex]\overline{x}\ \pm\ t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex] , where n = sample size.[tex]t_{\alpha/2}[/tex] = Two-tailed t-value for significance level of [tex](\alpha)[/tex] and degree of freedom df= n-1.[tex]s[/tex] = sample standard deviation.As per given , we have[tex]\overline{x}= 3.54[/tex] mms= 0.20 mmn= 25Significance level [tex]=\alpha=1-0.95=0.05[/tex]Since population standard deviation is not given , it means the given problem has t- distribution. Two-tailed t-value for significance level of [tex](0.05)[/tex] and degree of freedom df= 24:[tex]t_{\alpha/2\ ,df}=t_{0.025,\ 24}=2.0639[/tex]95% Confidence interval for population mean:[tex]3.54\ \pm\ (2.0639)\dfrac{0.20}{\sqrt{25}}[/tex] [tex]=3.54\ \pm\ (2.0639)\dfrac{0.20}{5}[/tex] [tex]=3.54\ \pm\ (2.0639)(0.04)[/tex] [tex]=3.54\ \pm\ 0.082556[/tex] [tex]=(3.54- 0.082556,\ 3.54+ 0.082556 )=(3.457444,\ 3.622556)\approx(3.46,\ 3.62)[/tex] Hence, the 95% two-sided confidence interval for the mean glass thickness = (3.46, 3.62)