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Dallas Colleges *

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2305

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Economics

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Apr 3, 2024

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pdf

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Uploaded by CaptainBook11588

A potato chip producer and its main supplier agree that each shipment of potatoes must meet certain quality standards . If the producer determines that more than 8 % of the potatoes in the shipment have " blemishes , " the truck will be sent away to get another load of potatoes from the supplier . Otherwise , the entire truckload will be used to make potato chips . To make the decision , a supervisor will inspect a random sample of potatoes from the shipment . The producer will then perform a significance test at the α = 0.05 level with a power of 0.62 . Describe a Type I and a Type II error in this setting . Type I Error - rejecting a shipment of potatoes that really was okay Type II Error - keeping a shipment of potatoes that really had too many blemishes . Which type of error is more serious in this case ? Explain . Type I would waste time and possibly slow production , and Type II would mean that customers get potentially bad chips . I would say Type II is more serious , as it impacts customers What is the probability of a Type I and Type II error in this situation ? Type 1 : Type.05 0.38 Give two ways you could increase the power of this test . You could take a larger sample size or you could make the significance level larger ( .10 instead of .05 ) . According to the National Campaign to Prevent Teen and Unplanned Pregnancy , 20 % of teens aged 13 to 19 say that they have electronically sent or posted sexually suggestive images of themselves . The counselor at a large high school worries that the actual figure might be higher at her school . To find out , she administers an anonymous survey to a random sample of 250 of the school's 2800 students . All 250 respond , and 63 admit to sending or posting sexual images . Carry out a significance test at the α = 0.05 significance level . P H · p = the true proportion of students at this school who have sent or posted sexual images HO : p = .20 Ha : p >.20 · A She took a random sample 250 students is less than 10 % of the school population of 2800 .20 ( 250 ) = 50
and .80 ( 250 ) = 200 are both greater than 10 N- We will do a one sample z test TShowswork here ! O - Sbow work here ! .252.20 2 = = 2.055 .20 ( 1-.20 ) 250 normalcdf lower : 2.055 upper : 10000 mean : 0 std dev : 1 M - reject the null S - Since the p value of .02 is less than a = .05 we reject the null hypothesis . There is convincing evidence that more than 20 % of the students at this school have sent or posted sexual images Based on your conclusion , what type of error ( Type I or Type II ) could you have made ? Type I Explain what this type of error would mean in context . We think more people have sent or posted sexual images than the national average at this school , but really they have not . A company has developed a new deluxe AAA battery that is supposed to last longer than its regular AAA battery . However , these new batteries are more expensive to produce , so the company would like to be convinced that they really do last longer . Based on years of experience , the company knows that its regular AAA batteries last for 30 hours of continuous use , on average . The company selects an SRS of 15 new batteries and uses them continuously until they are completely drained . The sample mean lifetime is 33.9 hours and the sample standard deviation is 9.8 hours , and a boxplot of the data is shown . P μ the true mean lifetime of the new AAA batteries in hours
T 0 10 20 30 40 50 60 ( b ) Battery life ( hours ) H · HO : μ = 30 Ha : μ > 30 A They took a random sample 15 batteries is less than 10 % of all the new batteries produced The graph shows no skew or outliers N- we will do a one sample t test T - Show work here ! O - Showзwork here ! t = 33.9-30 9.8 √15 tcdf lower : 1.54 upper : 10000 df : 14 M - Fail to reject S Since the p value of .073 is greater than a = .05 we fail to reject the null hypothesis . There is not significant evidence that the new batteries last longer than the old ones . Based on your conclusion , what type of error ( Type I or Type II ) could you have made ? Type II
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