In order to test the above proposition, state which statistics distribution you will use and justify your choice. (b) Test the above proposition at the 5% level of significance.

A new drug is being tested to see if it reduces the frequency of migraines.  Study participants were divided into two groups.  49 participants in group 1 received the medication; 42 participants in group 2 received a placebo.  After a period of six months, group 1 had a mean of 4 migraines.  It is known that the population standard deviation for this group is 1.3 migraines.  Group 2 had a mean of 5.4 migraines.  The population standard deviation for this group is 1.7 migraines.  Can we conclude that the medication reduces the population mean number of migraines?  Use αα =0.01.  Note: If t-test, then unequal variances are assumed. Question a)Let:     μ1μ1 = the population mean number of migraines with the medication           μ2μ2 = the population mean number of migraines with the placebo (Step 1) State the null and alternative hypotheses by selecting the appropriate symbol, and identify which tailed test:     H0:H0: μ1μ1         μ2μ2     H1:H1: μ1μ1         μ2μ2     Which tailed test…

You have obtained the number of years of education from one random sample of 38 police officers from City A and the number of years of education from a second random sample of 30 police officers from City B. The average years of education for the sample from City A is 15 years with a standard deviation of 2 years. The average years of education for the sample from City B is 14 years with a standard deviation of 2.5 years. Is there a statistically significant difference between the education levels of police officers in City A and City B?What is the appropriate test for this case? 2 sample z-testChi-square test     2-sample t-test2 sample paired t-test Carry out the test. The test statistic =   (round answer to two decimal places.)and the p-value is   (round answer to 2 decimal places)There     sufficient evidence at the 5% level to conclude that the education levels of police officers in City A and City B is significantly different.

A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 12 footballs were filled with helium to the recommend pressure and 15 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 267 yards with a standard deviation of 3 yards. The mean yardage for the air filled footballs was 241 yards with a standard deviation of 5 yards. Assume the populations are normal with equal variances. (a). Construct a 99% confidence interval for the mean difference in in yardage for the two types of footballs Lower bound (use 3 decimal places) Upper bound (use 3 decimal places) (b). What can you conclude about the sports writer's idea that helium footballs travel farther, on average? The helium footballs are no different than the other footballs, on average The other footballs travel farther on average than the helium footballs The helium footballs travel farther on average than the…

Consumer agencies claim that the mean lifespan of a dishwasher is 9.5 years. Your company manufacturers dishwasher and you have been asked to see if this claim is true. You randomly survey 20 households who have recently purchased a dishwasher and ask them how long their previous dishwashers lasted and you calculate a mean of 8.9 years with a standard deviation of 3.1. Is the consumer agency’s claim that a dishwasher lasts 9.5 year correct? What is the p-value for this claim? Consumer agencies claim that the mean lifespan of a dishwasher is 9.5 years. Your company manufacturers dishwasher and you have been asked to see if this claim is true. You randomly survey 20 households who have recently purchased a dishwasher and ask them how long their previous dishwashers lasted and you calculate a mean of 8.9 years with a standard deviation of 3.1. Is the consumer agency’s claim that a dishwasher lasts 9.5 year correct? What is the p-value for this claim?  0.8012  0.1988  0.3975  -0.8656

A study is done to determine if students in the California state university (CSU) system take longer to graduate, on average, than students enrolled in private universities using the significant level of 5%. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years for CSU and 1 year for private universities. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3. What is the decision rule of rejecting the null hypothesis

The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1825 pounds and a standard deviation of 70 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1825 pounds. To see if this is the case, 17 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1844 pounds. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1825 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0…

We want to test whether the mean fluoride levels in water fountains is worse in A or B. In order to test, a sample of 49 different water samples was taken from A and a sample was taken from 36 samples in B. A has a sample average of 2.3 micrograms of fluroide per deciliter of water and B has a sample average of 1.4 micrograms per deciliter of water. Further, A has a known standard deviation A=1.5 and B has a known standard deviation B=1.7. Find the p-value for the following hypothesis test: H0: uA-uB=0 vs Ha: uA-uB>0.