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Question Title:
Hypothesis testing and type errors
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<span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1. H<sub>0</sub>: The space being carpeted is 250 square feet, and the second measurement affirms this, within acceptable error.</span></p> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">H<sub>a</sub>: The space being carpeted is not 250 square feet, and the second measurement is significantly different.</span></p> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></p> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">2. H<sub>0</sub>: Drug B is less than or equal in effectiveness to Drug A.</span></p> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">H<sub>a</sub>: Drug B is more effective than Drug A.</span></p> <table class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt;" border="1" cellspacing="0" cellpadding="0"> <tbody> <tr> <td style="width: 155.8pt; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top" width="208"> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></p> </td> <td style="width: 155.85pt; border: solid windowtext 1.0pt; border-left: none; mso-border-left-alt: solid windowtext .5pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top" width="208"> <p class="MsoNormal"><span style="font-family: Calibri,sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">H<sub>0</sub> is true, H<sub>a</sub> is false (B <= A)</span></p> </td> <td style="width: XXX.XXXX; border: solid XXXXXXXXXX X.0pt; border-left: none; XXX-border-left-alt: solid XXXXXXXXXX .5pt; XXX-border-alt: solid XXXXXXXXXX .5pt; padding: XXX X.4pt XXX 5.4pt;" XXXXXX="XXX" width="208"> <p XXXXX="MsoNormal"><span style="font-family: XXXXXXX,sans-serif; XXX-ascii-theme-font: XXXXX-XXXXX; XXX-XXXXX-XXXXX-XXXX: XXXXX-XXXXX;">H<XXX>X</sub> is XXXXX, H<XXX>a</sub> is true (X &XX; X)</span></p> </td> </tr> <tr> <td style="width: 155.8pt; border: solid windowtext 1.XXX; border-top: XXXX; mso-border-top-alt: solid XXXXXXXXXX .5pt; XXX-border-XXX: solid XXXXXXXXXX .XXX; padding: XXX 5.4pt XXX X.XXX;" valign="top" width="XXX"> <p class="MsoNormal"><span style="XXXX-XXXXXX: Calibri,sans-serif; XXX-ascii-XXXXX-XXXX: minor-XXXXX; mso-hansi-XXXXX-XXXX: XXXXX-XXXXX;">XXXXXX H<XXX>0</sub> (X &XX;= A)</span></p> </td> <td style="width: XXX.XXXX; border-XXX: XXXX; border-left: none; border-XXXXXX: solid XXXXXXXXXX X.XXX; border-XXXXX: solid XXXXXXXXXX X.XXX; XXX-border-XXX-XXX: solid windowtext .5pt; mso-border-XXXX-alt: solid windowtext .XXX; mso-border-alt: solid windowtext .XXX; padding: 0in 5.4pt XXX 5.4pt;" valign="top" width="XXX"> <p XXXXX="XXXXXXXXX"><span style="font-family: Calibri,sans-serif; XXX-ascii-XXXXX-font: minor-latin; XXX-XXXXX-theme-XXXX: minor-XXXXX;">No XXXXX</span></p> </td> <td style="width: XXX.XXXX; border-top: none; border-left: XXXX; border-XXXXXX: solid XXXXXXXXXX X.0pt; border-XXXXX: solid XXXXXXXXXX X.0pt; XXX-border-top-alt: solid windowtext .5pt; mso-border-left-XXX: solid windowtext .5pt; mso-border-XXX: solid XXXXXXXXXX .XXX; padding: 0in X.XXX XXX 5.4pt;" XXXXXX="top" width="208"> <p class="MsoNormal"><span style="font-XXXXXX: XXXXXXX,sans-serif; mso-XXXXX-theme-font: minor-XXXXX; XXX-hansi-theme-XXXX: minor-XXXXX;">Type XX XXXXX</span></p> </td> </tr> <tr> <td style="width: 155.8pt; border: solid XXXXXXXXXX X.XXX; border-top: XXXX; mso-border-top-XXX: solid XXXXXXXXXX .XXX; mso-border-alt: solid XXXXXXXXXX .XXX; padding: 0in 5.XXX XXX 5.4pt;" XXXXXX="XXX" width="208"> <p XXXXX="XXXXXXXXX"><span style="font-family: Calibri,sans-XXXXX; mso-ascii-theme-font: XXXXX-latin; XXX-XXXXX-theme-XXXX: XXXXX-latin;">Accept X<sub>a</sub> (X &XX; A)</span></p> </td> <td style="width: 155.85pt; border-top: none; border-XXXX: none; border-XXXXXX: solid windowtext X.XXX; border-right: solid XXXXXXXXXX 1.XXX; XXX-border-top-XXX: solid XXXXXXXXXX .XXX; mso-border-XXXX-alt: solid XXXXXXXXXX .5pt; XXX-border-XXX: solid windowtext .XXX; padding: XXX 5.XXX 0in 5.XXX;" valign="XXX" width="XXX"> <p XXXXX="MsoNormal"><span style="font-family: XXXXXXX,sans-XXXXX; XXX-ascii-XXXXX-font: minor-latin; mso-hansi-theme-font: XXXXX-latin;">Type I error</span></p> </td> <td style="width: 155.85pt; border-XXX: XXXX; border-XXXX: none; border-bottom: solid windowtext X.0pt; border-right: solid XXXXXXXXXX 1.XXX; mso-border-top-XXX: solid windowtext .XXX; XXX-border-left-XXX: solid windowtext .XXX; XXX-border-XXX: solid XXXXXXXXXX .XXX; padding: 0in 5.XXX XXX 5.XXX;" XXXXXX="XXX" width="208"> <p XXXXX="MsoNormal"><span style="font-XXXXXX: Calibri,sans-serif; XXX-ascii-XXXXX-font: XXXXX-XXXXX; XXX-XXXXX-XXXXX-XXXX: XXXXX-XXXXX;">No error</span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span style="XXXX-family: Calibri,XXXX-XXXXX; XXX-ascii-theme-XXXX: XXXXX-XXXXX; XXX-hansi-XXXXX-font: XXXXX-XXXXX;"></span></p> <p XXXXX="XXXXXXXXX"><span style="font-XXXXXX: XXXXXXX,sans-XXXXX; mso-XXXXX-theme-XXXX: XXXXX-XXXXX; mso-XXXXX-XXXXX-XXXX: XXXXX-XXXXX;">Type I XXXXX XXXXX XX more severe, XX XXXX XXXXX XXXX XXX XXX drug XXX been XXXXXXX shown to XX more XXXXXXXXX XXXX XXX XXXXX XXXX. Drug A XXX XXXX XXXXX to be XXXXXXXXX, XXX XX it is replaced XX an ineffective XXXX B, XXXX XXX be very XXXXXXXXXXX. XX the XXXXX XXXX, XX XXXX X was falsely shown to XX equal or XXXX than Drug X in effectiveness, XXXX would be Type II error, XXXXX would XXX be XX XXXXXX. Drug X would XXX XXXXXXX XXXX X, but it XX XXXXX XXXX XXXX A is effective, so XXXX XXXX XXXXXXX in a decrease in XXXXXXXXXX, XXXXXX than XXX XXXXXXXX in XXXXXXXXXXXXX that the Type I XXXXX XXXXX XXXXXXX.</span></p> <p class="MsoNormal"><span style="XXXX-XXXXXX: XXXXXXX,sans-serif; XXX-XXXXX-XXXXX-XXXX: minor-XXXXX; mso-XXXXX-XXXXX-XXXX: minor-latin;"></span></p> <p XXXXX="MsoNormal"><span style="font-XXXXXX: Calibri,sans-XXXXX; XXX-ascii-XXXXX-font: XXXXX-latin; XXX-XXXXX-theme-font: minor-XXXXX;">X. X<sub>X</sub>: The bottles contain 6 XXXXXX of medicine XXX bottle.</span></p> <p class="XXXXXXXXX"><span style="font-XXXXXX: Calibri,XXXX-serif; mso-ascii-XXXXX-XXXX: XXXXX-XXXXX; mso-XXXXX-theme-XXXX: XXXXX-latin;">X<sub>a</sub>: XXX XXXXXXX XXXXXXX more than permitted XXXX X XXXXXX per XXXXXX.</span></p> <p class="MsoNormal"><span style="XXXX-family: XXXXXXX,sans-serif; XXX-XXXXX-theme-XXXX: minor-latin; mso-hansi-XXXXX-XXXX: minor-latin;"></span></p> <p XXXXX="MsoNormal"><span style="font-family: Calibri,sans-XXXXX; mso-ascii-XXXXX-font: minor-latin; mso-hansi-theme-font: XXXXX-latin;">XXXXXX XXX: X.95 X.XX 5.98 X.01 X.25 5.85 X.XX 6.05 X.XX X.XX</span></p> <p class="XXXXXXXXX"><span style="font-family: XXXXXXX,sans-XXXXX; mso-ascii-XXXXX-font: minor-latin; XXX-XXXXX-XXXXX-font: minor-latin;">XXXXXX distribution: XXXXXXXX XXXXXXXXX = X.3</span></p> <p XXXXX="XXXXXXXXX"><span style="font-family: XXXXXXX,XXXX-serif; XXX-XXXXX-XXXXX-font: minor-XXXXX; mso-hansi-XXXXX-XXXX: XXXXX-XXXXX;"></span></p> <p class="XXXXXXXXX"><span style="font-family: XXXXXXX,sans-XXXXX; XXX-XXXXX-theme-XXXX: XXXXX-latin; XXX-XXXXX-theme-font: minor-latin;">XXXX of sample XXX (X<sub>s</sub>) = X.XXX</span></p> <p XXXXX="XXXXXXXXX"><span style="font-XXXXXX: XXXXXXX,XXXX-serif; XXX-XXXXX-XXXXX-XXXX: XXXXX-latin; XXX-hansi-XXXXX-font: XXXXX-XXXXX;">Standard XXXXX (SE) = </span><span style="XXXX-XXXXXX: Calibri, sans-XXXXX; XXXXXXXXXX: #XXXXXX;">s/sqrt(n) = </span><span style="XXXX-XXXXXX: XXXXXXX,XXXX-serif; mso-ascii-theme-XXXX: XXXXX-latin; mso-hansi-XXXXX-font: XXXXX-XXXXX;">X.X / XXXX(XX) = 0.XXXX</span></p> <p XXXXX="MsoNormal"><span style="XXXX-XXXXXX: Calibri,sans-serif; mso-ascii-XXXXX-font: minor-XXXXX; mso-XXXXX-XXXXX-XXXX: minor-XXXXX;">X-XXXXX = (X<XXX>s</sub> - </span><span style="font-family: Calibri, XXXX-serif; XXXXXXXXXX-XXXXX: XXXXXXX; background-XXXXXXXXXX: initial; background-size: initial; XXXXXXXXXX-origin: initial; background-clip: XXXXXXX; background-XXXXXXXX: initial; XXXXXXXXXX-repeat: initial;">&XXXXX;</span><span style="XXXX-family: Calibri,XXXX-serif; XXX-XXXXX-theme-XXXX: XXXXX-latin; XXX-XXXXX-XXXXX-XXXX: minor-XXXXX;">) / SE = (X.XXX - 6.X) / X.0949 = -0.116</span></p> <p XXXXX="XXXXXXXXX"><span style="font-family: Calibri,XXXX-serif; XXX-XXXXX-theme-font: minor-XXXXX; mso-hansi-XXXXX-font: XXXXX-latin;">p-XXXXX = 0.XXX</span></p> <p class="XXXXXXXXX"><span style="font-XXXXXX: XXXXXXX,sans-serif; mso-XXXXX-XXXXX-XXXX: XXXXX-XXXXX; mso-XXXXX-XXXXX-XXXX: XXXXX-XXXXX;"></span></p> <p class="MsoNormal"><span style="XXXX-XXXXXX: Calibri,XXXX-XXXXX; mso-XXXXX-XXXXX-XXXX: minor-XXXXX; XXX-XXXXX-XXXXX-XXXX: minor-latin;">XXX p-XXXXX corresponding XX the X-score 0.-0.116 is X.0.XXX, XXXXX is not statistically significant at p<X.XX or p&XX;X.1. Therefore, there is not enough evidence to say XXXX XXX bottles XXX not filled adequately at 6 XXXXXX.</span></p> <p class="MsoNormal"><span style="font-XXXXXX: XXXXXXX,XXXX-serif; mso-ascii-theme-font: minor-latin; XXX-hansi-XXXXX-XXXX: minor-latin;"></span></p> <p class="MsoNormal"><span style="font-XXXXXX: XXXXXXX,sans-XXXXX; mso-ascii-XXXXX-XXXX: XXXXX-XXXXX; XXX-hansi-XXXXX-XXXX: minor-XXXXX;">7. X-XXXXX = (X - </span><span style="font-XXXXXX: Calibri, XXXX-XXXXX; background-image: XXXXXXX; XXXXXXXXXX-attachment: initial; background-XXXX: XXXXXXX; XXXXXXXXXX-XXXXXX: initial; XXXXXXXXXX-clip: initial; background-XXXXXXXX: initial; background-repeat: initial;">µ</span><span style="font-XXXXXX: XXXXXXX,sans-serif; mso-ascii-XXXXX-XXXX: XXXXX-XXXXX; mso-XXXXX-theme-XXXX: minor-latin;">) / s = (20 - 17) / X.4 = X.XXX</span></p> <p XXXXX="MsoNormal"><span style="font-family: Calibri,XXXX-serif; XXX-ascii-XXXXX-font: minor-XXXXX; mso-XXXXX-XXXXX-font: XXXXX-latin;"></span></p> <p XXXXX="MsoNormal"><span style="font-XXXXXX: Calibri,sans-XXXXX; mso-ascii-theme-XXXX: minor-XXXXX; XXX-XXXXX-theme-font: XXXXX-XXXXX;">8. XXX p-XXXXX corresponding XX a z-XXXXX XX X.882 XX 0.XXX. XXXX means that XXX XXXXXX of finding values XXXXX 20 in XXX XXXXXXXX XXXXXXXXXXXX centered XXXXXX 17 is 18.X%. X XX XXXXXX close to the mean, and is XXXXXX a XXXXXX standard XXXXXXXXX XXXX it, which can XX seen XX XXX z-XXXXX XXXXX X. XX checking X for error, XXX high p-value means that XXXXX is XX statistically significant error at any XXXXX (p&XX;0.XX or p<1). </span></p> <p XXXXX="XXXXXXXXX"><span style="font-family: Calibri,XXXX-serif; XXX-ascii-theme-font: minor-latin; mso-XXXXX-XXXXX-XXXX: minor-XXXXX;"></span></p> <p XXXXX="MsoNormal"><span style="XXXX-family: XXXXXXX,XXXX-serif; mso-ascii-theme-font: XXXXX-latin; XXX-XXXXX-XXXXX-XXXX: XXXXX-latin;">9. z-score = (X - </span><span style="XXXX-family: Calibri, sans-XXXXX; XXXXXXXXXX-image: initial; background-XXXXXXXXXX: XXXXXXX; XXXXXXXXXX-XXXX: initial; background-origin: XXXXXXX; XXXXXXXXXX-XXXX: XXXXXXX; background-position: XXXXXXX; background-repeat: XXXXXXX;">&XXXXX;</span><span style="font-XXXXXX: Calibri,sans-XXXXX; XXX-XXXXX-XXXXX-font: XXXXX-XXXXX; XXX-hansi-theme-XXXX: minor-XXXXX;">) / s = (12 - XX) / X.9 = -X.05</span></p> <p class="XXXXXXXXX"><span style="XXXX-XXXXXX: XXXXXXX,XXXX-serif; mso-XXXXX-theme-font: minor-XXXXX; XXX-XXXXX-theme-font: XXXXX-latin;">XXX p-value corresponding to this X-score XX -X.XX is 0.147, meaning that 14.7% XX XXXXXXXXXXX XXXX less than the XXX in XXXXXXXX. XXXXX this wouldnt XX XXXXXXXXXXXXX significant for error, it XXXXX indicates that XXXXX 85% of babysitters XXX XXXX more XXXX her per hour. I XXXXX consider XXXXXX her a XXXXX to $14 an XXXX, the XXXXXXX, which would XX appropriate XXXXX the XXXXXXXXXXXXX. Even though XXX XX XXXX about XXX XXXXXXXX XXXXXXXXX XXXX the XXXX, it XXXXX XXXXX XXX her XX believe she is underpaid XXXX a XXXXX majority of the XXXXX XXXXXXXXXXX are paid more than her.</span></p> <p XXXXX="XXXXXXXXX"><span style="XXXX-XXXXXX: XXXXXXX,XXXX-XXXXX; mso-XXXXX-theme-XXXX: XXXXX-XXXXX; mso-hansi-theme-font: XXXXX-XXXXX;"></span></p> <p class="MsoNormal"><span style="XXXX-XXXXXX: Calibri,sans-XXXXX; mso-XXXXX-XXXXX-font: minor-XXXXX; XXX-XXXXX-XXXXX-font: XXXXX-XXXXX;">XX. Standard XXXXX = s / sqrt(n) = XX / XXXX(100) = 3.X</span></p> <p class="MsoNormal"><span style="XXXX-XXXXXX: Calibri,sans-XXXXX; XXX-XXXXX-XXXXX-font: XXXXX-XXXXX; mso-XXXXX-XXXXX-font: minor-latin;">X-score = (X<sub>s</XXX> - </span><span style="XXXX-family: Calibri, XXXX-serif; background-image: initial; background-attachment: XXXXXXX; background-size: initial; XXXXXXXXXX-XXXXXX: XXXXXXX; background-clip: XXXXXXX; XXXXXXXXXX-position: XXXXXXX; background-repeat: initial;">&XXXXX;</span><span style="XXXX-family: Calibri,sans-serif; XXX-ascii-XXXXX-XXXX: XXXXX-XXXXX; XXX-XXXXX-theme-font: minor-XXXXX;">) / XX = (XXX - XXX) / X.X = XX</span></p> <p XXXXX="MsoNormal"><span style="XXXX-family: Calibri,sans-XXXXX; mso-ascii-XXXXX-XXXX: XXXXX-XXXXX; XXX-hansi-theme-font: XXXXX-XXXXX;">p-XXXXX XX very XXXXX to XXXX, XXXX XXXX X.XXXXX</span></p> <p class="XXXXXXXXX"><span style="font-family: XXXXXXX,XXXX-serif; XXX-XXXXX-XXXXX-font: minor-latin; mso-hansi-theme-font: XXXXX-latin;"></span></p> <p></p> <p class="XXXXXXXXX"><span style="font-family: XXXXXXX,XXXX-XXXXX; XXX-XXXXX-XXXXX-XXXX: XXXXX-latin; mso-hansi-theme-font: XXXXX-latin;">XXXXXXX XXX X-score XX XX, the XXXX XXXX the XXXX who XXXX through tutoring do XXXXXX XX XXX math portion XX. The almost-zero p-value XXXXXXXXX XXXX XXX XXXXX XX significant at XXXX the 5% level (p&XX;0.05) and the 1% XXXXX (p&XX;X.XX), meaning XXXX this XXXXXX XX XXXXXX error. XX XXXXXX XX said XXXX XXXXXXXXX if it XX a result XX the XXXXXXXX, XXXXXXX the sample is XXXXXX (XXXX kids XXXX XXXXXX XX for tutoring in the first XXXXX are in XXX XXXXXX). However, that XXXXXXXXXX itself XX XXXXXXXXX separate XXXX XXX normal distribution.</span></p>">
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