Hypothesis testFor a certain nationwide standardized test there are two commonly used preparation products on the market: StudyFocusand Prepara. A researcher in the Education department at a nearby university wants to determine if there is any differencebetween the two products on the mean score on the test by their users.The researcher obtains the scores on the test from a random sample of 16 users of StudyFocus and a random sample of 14users of Prepara. (These samples are chosen independently.) These data are shown in the table.?StudyFocusPreparaSend data to calculator408, 400, 460, 587, 485, 559, 470, 439, 453, 531, 491, 481, 529, 494, 581, 397510, 553, 504, 525, 549, 500, 525, 561, 510, 493, 498, 512, 517, 546VScoresSend data to ExcelPerform a two-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)ExplanationAssume that the two populations of scores are approximately normally distributed. Can the researcher conclude, at the 0.10level of significance, that there is a difference between the population mean of the scores on the test by the users ofStudyFocus and the population mean of the scores on the test by the users of Prepara?(a) State the null hypothesis Ho and the alternate hypothesis H₁.HoH₁ : 0H₁ :0(b) Determine the type of test statistic to use.(Choose one) ▼(c) Find the value of the test statistic. (Round to three or more decimal places.)(d) Find the two critical values. (Round to three or more decimal places.)and(e) At the 0.10 level of significance, can the researcher conclude that there is adifference between the mean score on the test by the users of StudyFocusand the mean score on the test by the users of Prepara?OYes ONOCheckI|xX0#0O0=0 OSOXSРŚO© 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center AccessibilityAa

Given that: Scores Study Focus 408, 400, 460, 587, 485, 559, 470, 439, 453, 531, 491, 481, 529, 494, 581, 397 Prepara 510, 553, 504, 525, 549, 500, 525, 561, 510, 493, 498, 512, 517, 546 For Study Focus: Evaluate Σx and Σx2 by using the following table: x x2 408 166464 400 160000 460 211600 587 344569 485 235225 559 312481 470 220900 439 192721 453 205209 531 281961 491 241081 481 231361 529 279841 494 244036 581 337561 397 157609 Σx=7765 Σx2=3822619 Compute the sample mean by using the formula: x¯=Σxn=776516=485.3 Compute the sample standard deviation by using the formula: S=Σx2- (Σx)2nn-1 =3822619- 776521615 =3822619-3768451.562515 =54167.437515 =60.09 For Prepara: Evaluate Σx and Σx2 by using the following table: x x2 510 260100 553 305809 504 254016 525 275625 549 301401 500 250000 525 275625 561 314721 510 260100 493 243049 498 248004 512 262144 517 267289 546 298116 Σx=7303 Σx2=3815999 Compute the sample mean by using the formula: x¯2=Σxn2=730314=521.6 Compute the sample standard deviation by using the formula: s2=Σx2- (Σx)2n2n2-1 =3815999- 730321413 =3815999-3809557.785713 = 6441.214313 =22.26(a) State the null and alternative hypotheses: H0:μ1=μ2H1:μ1≠μ2 This is two-tailed test. Thumb rule for equal variances: The ratio of larger variance to smaller variance must be less than 4. s12s22=60.09222.262=7.28>4 ∴Both variances are not equal. (b) T-test for unpaired samples. (c) Compute the test statistic: t=x¯1-x¯2-μ1-μ2s12n1+s22n2=485.3-521.6-060.09216+22.26214=-36.316.157=-2.246 (d) Find the degrees of freedom: df=s12n1+s22n22s12n12n1-1+s22n22n2-1=60.09216+22.26214260.09216216-1+22.26214214-1=19.5199≅20 Determine the critical values at 0.10 significance level and 20 degrees of freedom by using the following excel function: Critical values: +1.725 and -1.725(e) Make Decision: Rejection rule: Reject H0 if |calculated test statistic| > |tabulated critical value|, otherwise do not reject it. ∵2.246>1.725 Reject H0. Conclusion: There is enough evidence to conclude that there is significant differences between the two population means at 0.10 significance level. Thus, Yes is the correct answer.