Question

A. For this item and any of its parts assume population is known to be = 150.

1. If the distribution is normal, and a sample is desired which would generate condence interval with at a condence level 98% and margin of error, E, which is no more than 50, how large must the sample be? (Hint: It may help to answer A.4 rst.)

2. Now assume a sample has been drawn with the following values of size n=49 as shown below. 527 505 534 633 550 435 539 494 509 704 427 463 733 443 705 225 464 430 529 478 385 728 432 445 339 571 167 418 504 480 477 704 584 553 472 483 321 398 684 465 542 617 603 171 871 486 568 818 820. For your convenience P x = 25443 and P x2 = 14274731. What is the best point estimator for ?

3. What distribution, if any, can be used for condence levels or hypothesis tests in this situation, and why? State none, if appropriate, and explain why. Reminder: Distribution is NOT to be assumed normal here.

4. Regardless of previous answer, what standard normal (Z), critical value must be used g generate the 98% condence level?

5. Calculate the margin of error, E.

6. Calculate the condence interval.

Answer 1

2)Best point estimator for mean=25443/49=519.04

SD[X]=sqrt(21917.67)=148.05

3)Irrespective of what the original distribution is, as we are estimating the confidence intervals and hypothesis tests for the means, the mean would always follow a normal distribution.

4)Z=2.326

6)CI=[519.041-49.201,519.041+49.201]=[469.84,568.242]

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