In a laboratory, the time in minutes for an inspector to test an electrical circuit board is a conti

Question

In a laboratory, the time in minutes for an inspector to test an electrical circuit board is a continuous random variable $X$. The standard deviation of $X$ is $0.63$ and under ordinary conditions, the expected value of $X$ is $5.82$. As a result of the introduction of an incentive scheme, the laboratory supervisor claims that the inspector carries out the test more quickly. It is found that for a random sample of $150$ tests, the mean time taken to test an electrical circuit board is $5.74$. State appropriate hypotheses for the test of the claim, defining any symbols that you use.[2] Test whether the supervisor's claim is justified at $5$% level of significance.[3] Explain whether there is a need for the laboratory supervisor to know anything about the population distribution of $X$.[1] Two years later, a quality control officer took a random sample of $20$ tests and found that the mean time taken to test an electrical circuit board is $5.88$. He makes a claim that the mean time taken to test an electrical circuit board differs from $\mu_0$ mins. State two assumptions the quality control officer has to make in order to carry out a hypothesis test for this claim.[2] Given that the officer concludes that there is no reason to reject the null hypothesis at $1$% level of significance, find the range of values of $\mu_0$.[3]

Accepted Answer

(a)$\mu$ represents the population mean time taken to test an electric circuit board. $H_0 : \mu=5.82, H_1 : \mu<5.82 $ at 5% significance level. (b) Do not reject $H_0$. (c) No need, since n is large, by Central Limit Theorem $\bar{x}$ will be approximately normally distributed. (d)The time taken to test an electric circuit board follows a normal distribution. The population standard deviation of the time taken to test an electric circuit board is still 0.63. (e)5.52< $\mu_0$ <6.24

2025 ACJC P2 Q11

2025 ACJC P2 Q11