Question

please explain how to find p-value

What are you drinking? Environmental Protection Agency standards require that the amount of lead in drinking water be less than 1 micrograms per liter. Eleven samples of water from a particular source have the following concentrations, in units of micrograms per liter. Assume the population standard deviation is . If appropriate, perform a hypothesis test to determine whether you can conclude that the mean concentration of lead meets the EPA standards. Use the 0.03 level of significance and the P-value method with the TI-84 calculator. 11.9 149 14.8 16.7 8.9 12.9 8.8 13.9 17.9 9.9 16.1 Send data to Excel Part 1 of 6 Explain why it is necessary to check that the population is approximately normal before performing a hypothesis test. It is necessary to check that the population is approximately normal because the sample size is small 30 Part 2 of 6 Following is a dotplot of the data. Is it reasonable to assume that the population is approximately normal? 6 8 4 It is 10 12 14 16 18 20 reasonable to assume that the population is approximately normal. Part 3 of 6 State the appropriate null and alternate hypotheses. HOH = 15 H1 <15 This hypothesis test is a left-tailed test. Part: 3/6 Part 4 of 6 Compute the value. Round the P-value - 0 * value to at least four decimal places 3

Answer 1

Answers:

Ans a) Here the P-value for Part 1 is  1.00000

steps for calculating p-value in TI-84 calculator ( e.g.)

1) The majority of the commands used in this handout can be found under the DISTR menu which you can access by pressing [2nd] [VARS]. You should see the following:

Rey Fess s a rge screen NORMAL FLOAT AUTO REAL RADIAN MP TI-84 Plus C Silver Edition TEXAS INSTRUMENTS NORMAL FLOAT AUTO REAL RADIAN MP DISTR DRAH 18 normalpdf 2: normalcdf 3: invNorm 4:inuta 5: pdf 6: tcdf 7:x2 pdf 8:X?cdf 94F pdf DISTR DRAW 1: normalpdf 2: normalcdf 3: invNorm 4: invTC 5: tpdf 6: tcdf 7:X2pdf 8:X2cdfc 9Fpdf TABLE> STAT FLOT FI TILSET Y WINDOW FORVAT ROOM CALC 7 TRACE DD00:00:0:0 0000:00 OOO B00:0:0DDDD

2.

Left-tailed test (H1: µ < some number). The p-value would be the area to the left of the test statistic.

Rey Press Large screen NORMAL FLOAT AUTO REAL RADIAN MP TI-84 Plus C Silver Edition TEXAS INSTRUMENTS NORMAL FLOAT AUTO REAL RADIAN MP normalcdi lower: -10991 Upper:10^99 U: 15 0:.5/(10) Paste normalcdf lower: -10^91 upper:10^99 :15 0:.5/1 (10) Paste STAT POT FI TILSET WINDOW FORVAT ZOOM CALC 7 TRACE TABLE GRAW DOOD 0:0:0:0 0 Đc: POE

Ans b)  Here the P-value for Part 2 is  0.0965749

3. Two-tailed test (H1: µ ≠ some number):

Do the same as with a right-tailed or left-tailed test but multiply your answer by 2. Just recall that for a two-tailed test that:

• The p-value is the area to the left of the test statistic if the test statistics is on the left.

• The p-value is the area to the right of the test statistic if the test statistic is on the right.

Key Press History Large Screen NORMAL FLOAT AUTO REAL RADIAN MPO TI-84 Plus C Silver Edition TEXAS INSTRUMENTS NORMAL FLOAT RUTO REAL RADIAN MP normalcdf(17.1099.15..5/11) ...........5.85483065€ -37 .......1.170966138-36 normalcdf(17.1099, 15,.5/11 5.85483065E-37 Ans*2* ............ 1.17096613E-36. STAT PLOT FI TULSET P2 FORMAT CALC F4 TABLE GRAW DOOD:0:0:0:00 0 00:00:0:0:0:0D