Question
In: Statistics and Probability
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between...
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut butter, despite the labeling indicating that each jar should contain 16 oz. of peanut butter. He is wondering if Spiffy is cheating its customers by filling its jars with less product than advertised. He decides to measure the weight of 50 jars from the shipment and use hypothesis testing to verify this.
(a) Should the null hypothesis be rejected when the sample mean falls below or over a certain threshold? Should this threshold be below or above the value 16.0 oz?
(b) What is the distribution of X ̄, the sample mean?
(c) In his sample of 50 jars, the retailer finds an average weight of 15.84 oz and a sample standard deviation of 0.5 oz. He decides to use a significance level of 0.04. What is the conclusion from this hypothesis testing? Can you conclude that Spiffy is cheating its customers?
(d) What is the p-value? What is the meaning of this number?
(e) For what values of the sample mean would the null hypothesis be rejected?
(f) Calculate the probability of type II error if the true mean is 15.7 oz.
(g) Solve (c), (e) and (f) when the level of significance is 0.01. Is your new answer for (f) consistent with the p-value found in (g)? How is the probability of type II error affected when the probability of type I error changes?
Solutions
orchestra answered 2 years agoRelated Solutions
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between...
A retailer discovers that 3 jars from his last shipment of
Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut
butter, despite the labeling indicating that each jar should
contain 16 oz. of peanut butter. He is wondering if Spiffy is
cheating its customers by filling its jars with less product than
advertised. He decides to measure the weight of 50 jars from the
shipment and use hypothesis testing to verify this.
(a) What are the null and...
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between...
A retailer discovers that 3 jars from his last shipment of
Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut
butter, despite the labeling indicating that each jar should
contain 16 oz. of peanut butter. He is wondering if Spiffy is
cheating its customers by filling its jars with less product than
advertised. He decides to measure the weight of 50 jars from the
shipment and use hypothesis testing to verify this.
(a) What are the null and...
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between...
A retailer discovers that 3 jars from his last shipment of
Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut
butter, despite the labeling indicating that each jar should
contain 16 oz. of peanut butter. He is wondering if Spiffy is
cheating its customers by filling its jars with less product than
advertised. He decides to measure the weight of 50 jars from the
shipment and use hypothesis testing to verify this.
(a) What are the null and...
A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between...
A retailer discovers that 3 jars from his last shipment of
Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut
butter, despite the labeling indicating that each jar should
contain 16 oz. of peanut butter. He is wondering if Spiffy is
cheating its customers by filling its jars with less product than
advertised. He decides to measure the weight of 50 jars from the
shipment and use hypothesis testing to verify this.
(f) In his sample of 50...
Peanut Land Inc. produces all-natural organic peanut butter. The peanut butter is sold in 12-ounce jars....
Peanut Land Inc. produces all-natural organic peanut butter. The
peanut butter is sold in 12-ounce jars. The sales budget for the
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Dollar Sales ($)
January
80,000
176,000
February
45,000
99,000
March
40,000
88,000
April
42,000
92,400
Company policy requires that ending inventories for each month
be 10% of next month's sales. At the beginning of January, the
inventory of peanut butter is 31,000 jars.
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Peanut Land Inc. produces all-natural organic peanut butter. The peanut butter is sold in 12-ounce jars....
Peanut Land Inc. produces all-natural organic peanut butter. The
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first four months of the year is as follows: Unit Sales Dollar
Sales ($) January 70,000 147,000 February 65,000 136,500 March
60,000 126,000 April 62,000 130,200 Company policy requires that
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the beginning of January, the inventory of peanut butter is 31,000
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3. Peanut Butter and Jelly - Consider the case of a consumer that buys peanut butter...
3. Peanut Butter and Jelly - Consider the case of a consumer
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Suppose a large shipment of stereos contained 3% defectives. If a sample of size 396 is...
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Peanut butter price went from $1 per pound to $2, while its quantity demanded dropped from...
Peanut butter price went from $1 per pound to $2, while
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b in P=a-bQD
2) Denote the elasticity of peanut butter demand with
respect to price as EDP. What is the value of EDP at QD=330 million
pounds? What about at QD=300 million...
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