Question

A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 cm. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 cm. The population standard deviation is 0.44 cm. Determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance.

Group of answer choices

z = 2; therefore, reject H000. There is sufficient evidence at ααα = .05 to conclude that the lathe is NOT in perfect adjustment.

z = 2; therefore, do not reject H000. There is sufficient evidence at ααα = .05 to conclude that the lathe is NOT in perfect adjustment.

z = 2; therefore, reject H000. There is sufficient evidence at ααα = .05 to conclude that the lathe is in perfect adjustment.

z = 2; therefore, do not reject H000. There is sufficient evidence at ααα = .05 to conclude that the lathe is in perfect adjustment.

none of these answers are correct

Answer 1

Solution:- Given that, X = 6.08 6=0.44 n = 121 u = 6 a = 0.05 The null and alternative hypothesis, Ho: u=6 Ha: u 6 This is two-tailed test Test statistics z Z X-ul 61th = 6.08 - 6 0.44 / 1121 = 2 Z The test statistic Z - 2 P-value = 2 x PC Z > 2) 2xl-P(Z <2) 2 x1 - 0.9772 2 x 0.0228 = 0.0456 P-Value

d = 0.05 P-value =0.0456 0.0456 P- Value L0.05 <a Reject the null hypothesis. correct option:- 7 =2; therefore, reject Ho. There is sufficent evidence at x = 0.05 to conclude that the lathe is in perfect adjustment.