The head of a chocolate factory called you to check whether the production follows the requirements. Chocolate bars should individually weigh 43 grams. You have collected a sample of 105 bars, with an average weight of 39.5 grams and a standard deviation of 2.35 grams. Let Hold and pnew be the required weight of a chocolate bar and the average weight of sampled chocolate bars respectively. Let up be the mean of the differences between the required weight of a chocolate bar and the average weight of sampled chocolate bars. Part (A) Using a significance of 0.01, does the weight average match the requirements? Specify the null and alternative hypotheses. O (a) Ho: Hnew-Hold 20, H: Hnew Hold <0 O (b) Ho : µp <0, H1: up 2 0 O (c) Ho: µp 0, H1: µD= 0 O (d) Ho: µnew- Hold 0, H1: Hnew- Hold>0 O (e) Ho : µp > 0, H1 : µp S O () Ho: Hnew - Hold = 0, H1:µ-Hold #0 O (g) Ho : µnew – Hold 7 0, H1:µnew Hold = 0 O (h) Ho : Hnew Hold <0, Hị: Hnew Hold > 0 O Ho: HD= 0, H1 : µp#0 O ) Ho: µnew – Hold > 0, H1: Pnew - Hold <0 O (k) Ho : µD <0, H1 : µp > 0 O () Ho: HD 2 0, H1: Hp<0 Calculate the absolute value of the test statistic. number (rtol=D0.01, atol=D0.0001) Calculate the absolute value of the test statistic that would correspond to a= 0.01. number (rtol=D0.01, atol=D0.0001) State your decision. O (a) Reject HO

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The head of a chocolate factory called you to check whether the production follows the requirements.
Chocolate bars should individually weigh 43 grams. You have collected a sample of 105 bars, with an average
weight of 39.5 grams and a standard deviation of 2.35 grams.
Let Hold and plnew be the required weight of a chocolate bar and the average weight of sampled chocolate bars
respectively. Let up be the mean of the differences between the required weight of a chocolate bar and the
average weight of sampled chocolate bars.
Part (A) Using a significance of 0.01, does the weight average match the requirements? Specify the null and
alternative hypotheses.
O (a) Ho: Hnew-Hold 20, H: Hnew
Hold <0
O (b) Ho : µp <0, H1: up2 0
O (c) Ho: µp 0, H1: µD= 0
O (d) Ho: µnew - Hold <0, H1: Hnew Hold>0
O (e) Ho : µp > 0, H1 : µp S
O () Ho: Hnew
Hold = 0, H1 :H- Hold 70
O (g) Ho : µnew – Hold # 0, H1: µnew
Hold = 0
O (h) Ho : Hnew
Hold <0, Hı: Hnew
Hold > 0
O Ho: HD= 0, H1 : µp+ 0
O ) Ho: Hnew
Hold 0, H1: Pnew - Hold <0
O (k) Ho : µD <0, H1 : µp > 0
O () Ho: Hp > 0, H1: µp<0
Calculate the absolute value of the test statistic.
number (rtol=D0.01, atol=D0.0001)
Calculate the absolute value of the test statistic that would correspond to a= 0.01.
number (rtol=D0.01, atol=0.0001)
State your decision.
O (a) Reject HO
Transcribed Image Text:The head of a chocolate factory called you to check whether the production follows the requirements. Chocolate bars should individually weigh 43 grams. You have collected a sample of 105 bars, with an average weight of 39.5 grams and a standard deviation of 2.35 grams. Let Hold and plnew be the required weight of a chocolate bar and the average weight of sampled chocolate bars respectively. Let up be the mean of the differences between the required weight of a chocolate bar and the average weight of sampled chocolate bars. Part (A) Using a significance of 0.01, does the weight average match the requirements? Specify the null and alternative hypotheses. O (a) Ho: Hnew-Hold 20, H: Hnew Hold <0 O (b) Ho : µp <0, H1: up2 0 O (c) Ho: µp 0, H1: µD= 0 O (d) Ho: µnew - Hold <0, H1: Hnew Hold>0 O (e) Ho : µp > 0, H1 : µp S O () Ho: Hnew Hold = 0, H1 :H- Hold 70 O (g) Ho : µnew – Hold # 0, H1: µnew Hold = 0 O (h) Ho : Hnew Hold <0, Hı: Hnew Hold > 0 O Ho: HD= 0, H1 : µp+ 0 O ) Ho: Hnew Hold 0, H1: Pnew - Hold <0 O (k) Ho : µD <0, H1 : µp > 0 O () Ho: Hp > 0, H1: µp<0 Calculate the absolute value of the test statistic. number (rtol=D0.01, atol=D0.0001) Calculate the absolute value of the test statistic that would correspond to a= 0.01. number (rtol=D0.01, atol=0.0001) State your decision. O (a) Reject HO
number (rtol=D0.01, atol=D0.0001)
Calculate the absolute value of the test statistic that would correspond to a = 0.01.
number (rtol=D0.01, atol=D0.0001)
State your decision.
O (a) Reject HO
O (b) Cannot Reject HO
Part (B) Now, the head of the factory asks you to check whether the new production system reduces the
variability in the bar weight, if the old population standard deviation of the bars was 2.4 grams. Specify the null
and alternative hypotheses.
(a) Ho: onew 7 o old, H1 : Onew
O old
O (b) Ho : onew
Oold, H1: onew 7 o dld
O (c) Ho: Onew < O old, Hị: Onew 2 Oold
O (d) Ho : Onew 2 J old, Hị: Onew < old
O (e) Ho : Onew > Oold, H1: Onew
Oold
O (f) Ho : Onew o old, Hị: Onew > oold
Calculate the absolute value of the test statistic.
number (rtol=0.01, atol=D0.0001)
Calculate the absolute value of the test statistic that would correspond to a = 0.01.
number (rtol=D0.01, atol=D0.0001)
State your decision.
O (a) Cannot Reject HO
O (b) Reject HO
V VI
Transcribed Image Text:number (rtol=D0.01, atol=D0.0001) Calculate the absolute value of the test statistic that would correspond to a = 0.01. number (rtol=D0.01, atol=D0.0001) State your decision. O (a) Reject HO O (b) Cannot Reject HO Part (B) Now, the head of the factory asks you to check whether the new production system reduces the variability in the bar weight, if the old population standard deviation of the bars was 2.4 grams. Specify the null and alternative hypotheses. (a) Ho: onew 7 o old, H1 : Onew O old O (b) Ho : onew Oold, H1: onew 7 o dld O (c) Ho: Onew < O old, Hị: Onew 2 Oold O (d) Ho : Onew 2 J old, Hị: Onew < old O (e) Ho : Onew > Oold, H1: Onew Oold O (f) Ho : Onew o old, Hị: Onew > oold Calculate the absolute value of the test statistic. number (rtol=0.01, atol=D0.0001) Calculate the absolute value of the test statistic that would correspond to a = 0.01. number (rtol=D0.01, atol=D0.0001) State your decision. O (a) Cannot Reject HO O (b) Reject HO V VI
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