sis Testing ypothesis Tests for Goodness of Fit rections: Perform each test for

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sis Testing ypothesis Tests for Goodness of Fit rections: Perform each test for goodness of fit using the metho d of choice or the one assigned by your instructor. For each ex complete the following steps. a. State the null and alternative hypotheses. b. Determine which distribution to use for the test statistic, and staes level of significance. c. Find the expected value for each possible outcome, and calculate t test statistic. d. Draw a conclusion and interpret the decision. A school principal claims that the number of students who are tardy in her scholdist from month to month. A survey over the school year produced the following 05 level of sianificance test a teacher's claim that the number of tardy students

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here there are are four type of midnight shift i.e new moon (85), first quarter(66), full moon (97) and third quarter (68).total patients are =85+66+97+68=316. here

(a) null hypothesis H0: number of patients in all the shift are same ( i.e. not affected by phases of moon)

alternate hypothesis H1:  number of patients in all the shift are not same (i.e affected by phases of moon)

(b) here we use chi-square test and chi-square=sum((O-E)2/E) with k-1=4-1=3 df

with level of significance alpha=0.1

(c) under null hypothesis there is no effect of phases of moon, so each of phase will have equal frequency ( or patients) i.e. expected value of each of phase will be =316/4=79

chi-square= =sum((O-E)2/E) =8.23 with k-1=4-1=3 df

(d) critical chi-square(0.1,3)=6.25 is less than calculated chi-square=8.2278, so we fail to accept H0 and conclude that number of patients are affected by phases of moon at 10% level of significance

observed(O) Expected (E) (O-E) (O-E)2/E new moon 85 79 6 0.4557 first quarter 66 79 -13 2.1392 full moon 97 79 18 4.1013 third quarter 68 79 -11 1.5316 sum 316 316 0 8.2278

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