Macarthurs, a manufacturer of ropes used in abseiling, wished to determine if the production of their ropes had seen an increase in the average breaking strength above their specifications. All ropes being manufactured were required to have a breaking strength of 235.0 kilograms and a standard deviation of 18.5 kilograms. They planned to test the breaking strength of their ropes using a random sample of forty ropes and were prepared to accept a Type I error probability of 0.01.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of the sample mean used in testing the claim (to two decimal places). If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of the sample mean used in testing the claim (to two decimal places). If there is no (theoretical) upper boundary, type gt in the box.

5. If the average breaking strength found from the sample is 245.0 kilograms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected when the rope being tested included a new synthetic fibre, could it be concluded that adding the new synthetic fibre had affected the breaking strength of the rope at the 1% level of significance? Type yes or no

?

The fuly amount of smantis, X, In meands for the Colleges WI-FIlighten has spams distribution with huge parameters ] and soshe purwater / # 2. K has probability danity function: aj If XXX:, XXXs are the downtimes of each of the 5 days of the workweek, and if daily downtimes are independent of one another then what is the probability that X1X2X; XX, are all greater than 2 seconds? bj What theorem permits us to treat the sum or the sample mean of more than 30 independent, identically distributed random variables as if they were normal random variables? Central Limit Theorem Law of Large Numbers Chebychev's Theorem Convolution Theorem Monte Carlo Theorem c) Suppose we randomly select 64 independent downtimes. What is the approximate probability that the total downtime for the 64 days is between 375 and 400 seconds. That is, if X X2 .....Xeg are the downtimes of 64 days then what is the approximate probability that 375 -2.64) 3. Given the z follows a standard normal distribution, use the Table to determine: Prob( -2.2 -13)D Question 2 3 pts What Does the Standard Normal Distribution Tell Us? When we have the standard normal distribution, we know . the mean is . the standard deviation is . any normal distribution can be converted to a standard normal distribution by converting all the measurements to standard