Question 14 (1 point) we would like to conduct a hypothesis test at the 2% level

Question

Question 14 (1 point) we would like to conduct a hypothesis test at the 2% level of significance to determine whether the true mean pH level in a lake differs from 7.0. Lake pH levels are known to follow a normal distribution. We take 10 water samples from random locations in the lake. For these samples, the mean pH level is 7.3 and the standard deviation is 0.37. Using the critical value approach, the decision rule would be to reject Ho if the test statistic is: O A) less than -2.326 or greater than 2.326 O B) less than -2.398 or greater than 2.398 O c) less than -2.564 or greater than 2.564 O D) less than -2.764 or greater than 2.764 O E) less than -2.821 or greater than 2.821 Save Question 15 (1 point) The manager at a car assembly plant believes that the mean assembly time for a car is greater than the target time of 35 hours. We record the assembly times for a sample of ten cars. The mean and standard deviation assembly times of these ten cars are calculated to be 37 hours and 5 hours, respectively. Assembly times are known to follow a normal distribution. At the 5% level of significance, we have: O A) insufficient evidence that the true mean assembly time is greater than 35 hours, since the P-value is betweer 0.05 and 0.10 sufficient evidence that the true mean assembly time is greater than 35 hours, since the P-value is between 0.10 and 0.15 B) O c) insufficient evidence that the true mean assembly time is greater than 35 hours, since the P-value is betweer 0.10 and 0.15 O D) sufficient evidence that the true mean assembly time is greater than 35 hours, since the P-value is between 0.20 and 0.30 O E) insufficient evidence that the true mean assembly time is greater than 35 hours, since the P-value is between 0.20 and 0.30 Save

Explanation / Answer

Question 14:

As we are trying to test here whether the true PH level differ from 7, therefore this is a two tailed test. As we are doing the test at 2% level of significance and the underlying distribution is a normal distribution, from the standard normal tables, we get:

P( -2.326 < Z < 2.326 ) = 0.98

But as we are not given here that population standard deviation, therefore we will have to use the t distribution here to perform the hypothesis test. For n-1 = 9 degrees of freedom, we get from the t distribution tables that:

P( -2.821 < t9 < 2.821 ) = 0.98

Therefore we reject the null hypothesis when the test statistic lies outside the above interval that is when the t value is less than -2.821 or greater than 2.821

Therefore E is the correct answer here.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.