STATISTICS 200 Week 5: Assignment – Overview of Hypothesis Testing & Type I and II Error

#1 Points possible: 2. Total attempts: 3 At most 70% of Internet users pay bills online. Express the null and alternative hypotheses in symbolicform for this claim (enter as a percentage).H0 : pH1 : pUse the following codes to enter the following symbols:? enter >=? enter <=? enter !=#2 Points possible: 2. Total attempts: 3 A commonly cited standard for one-way length (duration) of school bus rides for elementary schoolchildren is 30 minutes. A local government office in a rural area randomly samples 100 elementaryschool children in their district and find an average one-way commute time of 38 minutes with astandard deviation of 8 minutes.Which of the following is the correct set of hypotheses for testing if the average commute time ofelementary school students in this district is different than the commonly cited standard of 30 minutes?H0: µ = 30; HA: x = 38H0: µ = 30; HA: µ > 30HA: µ = 30; H0: x ? 30H0: x = 38; HA: µ = 30H0: µ = 30; HA: µ ? 30 #3 Points possible: 2. Total attempts: 3 A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered twoperspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. Oneposition supported running on soft surfaces to relieve joints that were in recovery from injury. Thesecond position supported running on hard surfaces since soft surfaces can be uneven, which may makeworse those injuries a soft surface was intended to help.Suppose we are given sufficient funds to run an experiment to study this topic. With no studies tosupport either position, which of the following hypotheses would be appropriate?The first position is more sensible, so this should be a one-sided test. In this case, we should formthe alternative hypothesis around the second position.Because we would be interested in any difference between running on hard and soft surfaces, weshould use a two-sided hypothesis test.Because there is uncertainty, we should postpone defining the hypotheses until after we collectdata to guide the test.The second position makes the more sense, so this should be a one-sided test. In this case, weshould form the alternative hypothesis around the first position. #4 Points possible: 2. Total attempts: 3 If your null and alternative hypothesis are:H0 : µ = 2H1 : µ > 2 Then the test is:left tailedtwo tailedright tailed #5 Points possible: 2. Total attempts: 3 A commonly cited standard for one-way length (duration) of school bus rides for elementary schoolchildren is 30 minutes.A local government office in a rural area conducts a study to determine if elementary schoolers in theirdistrict have a longer average one-way commute time. If they determine that the average commute timeof students in their district is significantly higher than the commonly cited standard they will invest inincreasing the number of school busses to help shorten commute time. What would a Type 2 error meanin this context?The local government decides that the average commute time is 30 minutes.The local government decides that the data provide convincing evidence of an average commutetime higher than 30 minutes, when the true average commute time is in fact 30 minutes.The local government decides that the data do not provide convincing evidence of an averagecommute time higher than 30 minutes, when the true average commute time is in fact higher than30 minutes.The local government decides that the data do not provide convincing evidence of an averagecommute time different than 30 minutes, when the true average commute time is in fact 30minutes. #6 Points possible: 2. Total attempts: 3 Food inspectors inspect samples of food products to see if they are safe. This can be thought of as ahypothesis test with the following hypotheses.H0: the food is safeHa: the food is not safeThe following is an example of what type of error?The sample suggests that the food is safe, but it actually is not safe.type Itype IInot an error #7 Points possible: 2. Total attempts: 3 If your claim is in the null hypothesis and you fail to reject the null hypothesis, then your conclusionwould be:There is not sufficient sample evidence to support the original claimThere is sufficient evidence to warrant rejection of the original claimThe sample data support the original claimThere is not sufficient evidence to warrant rejection of the original claim