Tutorial 08_1_2018_SOLUTIONS_18th April.pdf

Let x breaking strength of the fabric kg xn μ 35 n49

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Let X = breaking strength of the fabric (kg) X~N ( μ , 3.5) n=49 α = 0.05 σ known, so use Z -distribution Claim: μ ≠ 30 Must be H 1 since it does not have an ‘equals’ in it. Step 1: Hypotheses H o : μ =30 H 1 : μ ≠ 30 Step 2: Test statistic 0 X Z n Z calc = 29.3−30 3.5 √49 = -1.40 Step 3: Critical Value Z crit = Z 0.025 = 1.96 Step 4: Decision Rule and Decision Reject H 0 if Z calc < -Z crit or Z calc > Z crit Since -1.40 < -1.96, we cannot reject H 0
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ETF1100 Business Statistics SOLUTIONS Tutorial 8 3 Step 5: Conclusion We cannot reject H 0 at the 5% level of significance. The sample DOES NOT provide enough evidence against H 0 . That is, the mean breaking strength is NOT different from 30 Kg. The new machine is producing cloth according to the manufacturer’s specifications. Q8.3 Hoping to lure more shoppers downtown, a regional city council builds a new public parking garage close to the main shopping street. The city plans to pay for the building through parking fees. The consultant who advised the city on this project predicted that parking revenues would average $970 a day. For a random sample of 30 weekdays, the daily fees collected averaged $964 with a standard deviation of $20. a) Perform a hypothesis test to determine whether there is evidence at the 5% level of significance that the average revenue is lower than the consultant predicted. Use the critical value approach and ensure that you clearly state your hypotheses, show ALL steps, ALL your working AND interpret your conclusion in context of this question. Let X = daily parking fees collected ($) Since the distribution of X is unknown, we can invoke CLT as the sample size is sufficiently large (n =30). The CLT states that if n>30, then the distribution of the sample mean ( 𝑋 ̅ ) is approximately normally distributed.
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