Question

Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, samples of 600 and 500 planks, respectively, were examined under the old and new methods. Sixty-two of the 600 planks were scrapped under the old method, whereas 34 of the 500 planks were scrapped under the new method. a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) Confidence interval is 90 to b. Select the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively. Ho: p1-p2 = 0; HA p1-p2#0 Ho: P1-P2 S0; HA: P1-P20 Ho: P1-P2 20; HA: P1-P2 0 C. Using the part a results, can we conclude at the 10% significance level that the scrap rate of the new method is different than the old method? We (Click to select B proportions are different between the old and new methods HO. At the 10% significance level, we (Click to select) concludethe

Answer 1

Sol:

In Ti83 go to STAT>TESTS>2-PROPZINT

enter the data as:

TEXAS INSTRUMENTS TI-83 Plus 2-ProFZInt ×1162 n1:600 x2:34 n2:50 C-Level:.90 Calculate = MINDO) ZOOM. TRACE GRAPH 2 QUIT INS MODE DEL A-LOCK LINK UST ALPHA XIe, STAT TEST ANGLE 8 DRAW C DISTR MATH APPSPRGM VARS CLEAR

TEXAS INSTRUMENTS TI-83 Plus 2-ProFZInt 00775, . 06291) P1.1033333333 n1 602 n2=500 WINDOWZOOM TRACE GRAPH 2 QUIT INS 2nd MODE DEL

ANSWER:

0.00775*100,0.06291*100

=0.78% to 6.29%

ANSWER:

90% confidence interval for p1-p2 is

0.78% to 6.29%

Solutionb:

H0:p1-p2=0

Ha:p1-p2 not =0

OPTION A

Solutionc:

in ti 83 go to

TESTS>2-PROP Z TEST

TEXAS INSTRUMENTS TI-83 Plusx 2-ProFZTest × 1 : 62 n1:600 x2: 34 n2:500 Draw ZOOIA RACE GRAPH QUIT INS MODE DEL A-LOCK LINK LUST ALPHA XIe, STAT MATH APPSPRGM VARS CLEAR

TEXAS INSTRUMENTS TI-83 Plus 2-ProFZTest z=2. 067469482 FE,386898043 . 1033333333 ↓ 0872727273 ZOOIA TRACE GRAPH QUIT INS MODE DEL

You will get

z=2.067

p=0.0387

alpha=0.10

p<alpha

Reject Ho.

ANSWER;

We reject Ho.at he 10% significance level,w can conclude the proportions are different between the old and new methods