(Solved): Interval Frequency <3.872 3 3.872-3.916 7 3.917-3.948 10 3.949 ...

​​​​​​​Interval Frequency
<3.872 3
3.872-3.916 7
3.917-3.948 10
3.949-3.975 10
3.976-4.000 4
4.001-4.025 7
4.026-4.052 2
4.053-4.084 5
4.085-4.128 1
>4.128 1

A company manufactures four-inch-diameter wooden dowels. The quality control procedures aimed at maintaining the 4-inch diameter are only valid if the diameters have a normal distribution. The quality control manager recently obtained the summary diameters taken from randomly selected dowels on the production line, as shown in the accompanying table. The dowel diameters are specified to have a normal distribution with a mean of 4 inches and a standard deviation of 0.10 . Determine if the distribution of the 4-inch dowels is currently adhering to specification. Use a chi-square goodness-of-fit test and a significance level of 0.05 . Click the icon to view the data table. State the appropriate null and alternative hypotheses. Choose the correct answer below. A. ${\mathrm{H}}_0$ : The diameter is normally distributed with $\mu =4$ and $\sigma =0.10$. ${\mathrm{H}}_{\mathrm{A}}$ : The diameter is not normally distributed with $\mu =4$ and $\sigma =0.10$. B. ${\mathrm{H}}_0$ : The diameter is not normally distributed with $\mu =4$ and $\sigma =0.10$. ${\mathrm{H}}_{\mathrm{A}}$ : The diameter is normally distributed with $\mu =4$ and $\sigma =0.10$. C. ${\mathrm{H}}_0:\mu \ne 4$ ${\mathrm{H}}_{\mathrm{A}}:\mu =4$ D. ${\mathrm{H}}_0:\mu =4$ ${\mathrm{H}}_{\mathrm{A}}:\mu \ne 4$ The test statistic is ${\chi }^2=$ (Round to three decimal places as needed.)