S. Suppor, according to a 2016 demographic report, the average U. S. bousebold s
ID: 2934780 • Letter: S
Question
S. Suppor, according to a 2016 demographic report, the average U. S. bousebold speads 0 per day. Suppose you reoently took a raadom sample of 30 households in Huntsville 800 per sad the results revealed a mean of $86.50. Suppose the standard deviation is known to be 14.50. Using a 0.05 level of significance, can it be concluded that the average amount spest per day by U.S. honseholds has decreased? 6. Suppose a prodactioe line operates with a meas filling weight of 16 ounces per costainer. Since over- or under-filling can be dangerous, a quality coutrol inspector samples 30 itens to determine whether or not the filling weight bas to be adjusted. The sample revealed a mean of 16.32 ounces and the standard deviation 0.8 ounces Using a 0.10 level of significance, can it be concluded thst the process is out of control (sot equal to 16 ounoes)1 . The salestman claims that the average weight of each can of the drink is at least 20 ounce, and the standard deviation is 3 ounce. To test the claim, you have checked 20 cans, and found the average is only 18.6 ounce. Can you reject the claim at significance level 0.05? 8. A professor wants to kaow if her introductory statistics class has a good grasp of basic math. 10 students are choeen at random from the class and given a math proficiency test. The peofessor wants the class to be able to score above 70 on the test. From these 10 students, she fiad average is: 73.17, standard deviation is: 13.16. Can the professor have 90 peroent contiensoe that the mesua seore for the class on the test would be abowe 70?Explanation / Answer
Question 5
Here sample mean x = $ 86.50
sample size = 30
Population standard deviation = $ 14.50
Here
H0 : = $ 90
Ha : < 90
Where is average amount spent per day by US houshold.
Standard deviation of sample mean se0 = / sqrt(30) = 14.50/ sqrt(30) = $ 2.647
Test statistic
Z = (86.5 - 90)/ 2.647 = -1.32
p - value = Pr(Z < -1.32) = 0.0934
so here p - value > 0.05 so it is not significant so we can conclude that there is not significant difference in mean amount spent by US household.
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