ORM.S.INV(α) (z-score should be negative) ORM.S.INV(1-α) (z-score should be positive) .INV(α,df) (t-score should be negative) .INV(1-α,df) (t-score should be positive) Two-tailed tests: z α/2 = NORM.S.INV(α/2) (both the + and – are critical) Two-tailed tests: t α/2 = T.INV(α/a,df) ((both the + and – are critical)
Formula for the z-Test statistic for a Hypothesis Test for the proportion (zp) Upper-tailed test: reject H 0 when test statistic (z xbar , t xbar , or z p ) > critical test statistic (z α o Lower –tailed test: reject H 0 when test statistic (z xbar , t xbar , or z p ) < critical test statistic (z α Upper-tailed test: reject H 0 when test statistic (z xbar , t xbar , or z p ) < OR > critical test statisti H 0 n p p p p z H H H p ) 1 ( 0 0 0
Two tailed Test (insert the symbols) Two tailed, Upper Tailed, or Lower Tailed? Ho: u = 56 This test would be used by someone that wants to prove that the average is __ different than 56. H1: u /= 56 Ho: u <= 56 Upper ; alternative hypothesis has > symbol. This test would be used by someone that wants to prove that the average is ___ higher _ than 56. H1: u > 56 Ho: u >= 56 Lower ; alternative hypothesis has < symbol. This test would be used by someone that wants to prove that the average is _ less ____ than 56. H1: u < 56
or t α ) α or t α ) tic (z α/2 or t α/2 )
Rules what we want to prove goes in the alternative the equals always goes in the null 1 <= 0.7 the proportion of people who plants to be E-filers for t > 0.7 is greater than 70% Test: One tail Upper 2 = 2.9 must divided Alpha/2 to get upper and lower -zCri /= 2.9 so the average #of tv's in the home of consumers com Test: Two Tail Test 3 >= 60 < 60 Test: One tail Lower critical zscore should be negative. the current average time on the market is less than 60 days. H 0 H 1 H 0 H 1 H 0 H 1
the next tax season itical & Zscore mcast is not 2.9 One-Tailed Test: Find z-score at __ α _______ in the tail Two-Tailed Test: Find z-score with _ α /2 ______ in the tail
type of test: n= std dev= u= a=alpha type of test: n= u= std dev= a= type of test: n= u= std dev= a= H 0 H 1 H 0 H 1 H 0 H 1
u <= 40 u > 40 one tail upper the average age of customers is greater than 40 yrs old. 60 8 42.7 0.02 u = 5 u /= 5 Two tail test ZINCO'S CUSTOMERS DOESNOT SPEND FIVE MINUETS FOR SERVICE. 45 5.5 1.7 0.02 u >= 20 u < 20 one tail lower THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN. 45 18.3 5 0.05
Step 1 Identify the Null and Alternative Hypothesis u >= 20 u < 20 type of test: type of test: one tail lower THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 Step 2 alpha α 0.05 Step 3 Determine the appropriate critical z-score z at alpha NORM.S.INV(ALPHA) -1.644854 -1.645 Step 4 Calculate the appropriate test statistic (test zscore) n 45 xbar 18.3 pop std dev 5 numerator -1.7 xbar - uHo denominator 0.745355992 std error test zscore -2.28078934 Step 5 Compare Test Zscore againts Critical Zscore test zscore critical zscore -2.28078934 < -1.644853627 Step 6 State your conclusions H 0 H 1 Set a value for the significance level, α n σ μ x z H x 0
we reject the Null and conclude in the Alternative that, THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN.
STP1 u >= 20 u < 20 type of test: one tail lower THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN.
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- Null hypothesis, Statistical hypothesis testing, Critical Zscore, test zscore