INFERENCES ABOUT THE POPULATION MEAN TABLE 3, TABLE 4 ILAST ROW AND CLASS NOTES
ID: 3336045 • Letter: I
Question
INFERENCES ABOUT THE POPULATION MEAN TABLE 3, TABLE 4 ILAST ROW AND CLASS NOTES ARE REQUIRED. 130 POINTS-3+3+4+5+5+5+51 A SAMPLE OF 25 FAMILIES WAS DRAWN FOR ANALYSIS OF THE AVERAGE GROCERY SPENDING. ASSUME THAT THE INDIVIDUAL WEEKLY RECORDS ARE NORMALLY DISTRIBUTED, WITH THE UNKNOWN POPULATION AVERAGE AND POPULATION STANDARD DEVIATION OF $40. SAMPLE SUMMARIES WERE (SAMPLE MEAN)-$154 AND (SAMPLE STANDARD DEVIATION)-$50 DO YOU HAVE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE WOULD BE ABOVE $140? USE THE SIGNIFICANCE LEVEL OF 5%. SHOW THE FOLLOWING ELEMENTS OF YOUR DECISION-MAKING PROCESS. POPULATION STANDARD DEVIATION OF THE SAMPLE MEAN NULL HYPOTHESIS ALTERNATIVE CRITICAL VALUE REJECTION RULE [WHEN THE NULL HYPOTHESIS WILL BE REJECTED TEST STATISTIC VALUE DECISION: TO REJECT OR NOT TO REJECT.Explanation / Answer
Nul HYpothesis : H0 : = $140
Alternative Hypotheiss : Ha : > $140
Critical value :
Here population standard deviation is given so we will use Z test here
Zcr for alpha level 0.05 is = 1.645 [ one sided test]
Rejection Rule:
Null hypothesis shall be rejected if test statistic Z > 1.96
Test statistic
Standard error of the mean sem= s/ sqrt(N) = 40/ sqrt(25) = 40/5 = 8
Z = (xbar - H)/ sem = (154 - 140) / 8= 1.75
so here Z > Zcritical
so we shall reject the null hypothesis and claim that mean grocery spending is more than $ 140.