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AP StatisticsChi-Square Goodness-of-Fit TestName:_________________1. I m sorry of the complying with statements about the chi-square (χ2) circulation is true?A. The density curve of the χ2 distribution is symmetric.B. As the variety of degrees of freedom increases, the top C vital value of the χ2distribution rises for every fixed value C.C. No (A) no one (B) is true.2. Indigenous experience, the owner of an ice-cream shop has uncovered that 60% of all sales the ice-cream conesare because that one-scoop cones, 30% space for two-scoop cones, and the remaining 10% are for three-scoopcones. Recently, the shop included frozen-yogurt cones come its menu. A random sample that 250 frozenyogurt cone sales revealed the complying with distribution:The owner wishes to understand whether the pattern of sales because that frozen-yogurt cones different from that of icecream cones. Let p1, p2, and p3 it is in the proportions that sales the one-scoop, two-scoop, and three-scoopfrozen-yogurt cones, respectively. How would we write the null and alternate hypotheses for agoodness-of-fit test based upon the χ2 distribution?A. H0: p1 = 0.6, p2 = 0.3, p3 = 0.1.Ha: At least one that the proportions p1, p2, and p3 differs from the value declared in H0.B. H0: p1 = 0.6, p2 = 0.3, p3 = 0.1.Ha: p1 ≠ 0.6, p2 ≠ 0.3, p3 ≠ 0.1.C. H0: Ice-cream cone sales and also frozen-yogurt cone sales space independent.Ha: Ice-cream cone sales and also frozen-yogurt cone sales are dependent.3. From experience, the owner of one ice-cream shop has uncovered that 60% of every sales that ice-cream conesare for one-scoop cones, 30% are for two-scoop cones, and also the continuing to be 10% room for three-scoopcones. Recently, the shop included frozen-yogurt cones come its menu. A arbitrarily sample the 250 sales offrozen-yogurt cones revealed the complying with distribution:The owner wishes to recognize whether the pattern of sales for frozen-yogurt cones differs from that of icecream cones. In a goodness-of-fit test based upon the χ2 distribution, the supposed count for "number oftwo-scoop frozen-yogurt cone sales" would certainly beA. 84.B. 75.C. 83.33.4. A fast-talking salesman offers you a table of "random digits" the comes v a "guarantee" ofrandomness. Friend don"t trust him, so you urge on experimentation the table through generating a sample that 300 digitsfrom that rows. Here are the resulting frequencies that the 10 number 0 through 9 in your sample that size300:With the salesman getting much more nervous by the minute, you then conduct a goodness-of-fit check of thenull hypothesis that the table"s digits are indeed random (that is, the the probability of seeing any type of ofthe 10 digits 0 v 9 in a single observation is equal to 1/10 or 0.10) against the alternate thatthey room not random. What is the value of the χ2 test statistic in this case?A. 0B. 0.271C. 8.135. A fast-talking salesman offers you a table that "random digits" the comes v a "guarantee" ofrandomness. You don"t trust him, so you insist on testing the table by generating a sample that 300 digitsfrom that rows. Below are the result frequencies that the 10 digits 0 through 9 in your sample that size300:With the salesman getting more nervous by the minute, you then conduct a goodness-of-fit test of thenull theory that the table"s digits are indeed random (that is, that the probability the seeing any ofthe 10 number 0 v 9 in a single observation is equal to 1/10 or 0.10) against the alternate thatthey are not random. What execute you conclude?A. Over there is no reason to doubt the the table"s number are indeed random: the P-value of the check isgreater 보다 0.10.B. The table"s digits are rather random, but you should regard the results with some caution: the Pvalue that the test is in between 0.05 and also 0.10.C. The salesman is a crook since the table"s digits do not show up to it is in random: the P-value the the testis at most 0.05.6. A study was conducted to recognize where moose are discovered in a region containing a big burnedarea. A map the the study area to be partitioned into the following four habitat types.(1) within the melted area, not close to the sheet of the shed area,(2) inside the shed area, near the edge,(3) external the shed area, close to the edge, and(4) exterior the melted area, not near the edge.The figure listed below shows these 4 habitat types.The proportion of total acreage in each of the habitat varieties was figured out for the research area. Making use of anaerial survey, moose locations were observed and classified into one that the 4 habitat types. Theresults are provided in the table below.Habitat Type1234TotalProportion of full Acreage0.3400.1010.1040.4551.000Number the Moose Observed25223040117The researcher who are conducting the examine expect the variety of moose observed in a habitat typeto it is in proportional come the quantity of acreage that that kind of habitat. 1) room the data constant with thisexpectation? 2) conduct an appropriate statistical check to assistance your conclusion. I think theconditions because that inference room met. 3) Explain, loved one to the relationship of complete acreage, i m sorry habitattypes walk the moose seem come prefer.7. Contestants on a game display spin a wheel prefer the one presented in the number below.Each that the four outcomes ~ above this wheel is equally likely and outcomes space independent from one spinto the next.The contestant spins the wheel.If the an outcome is a skunk, no money is won and also the contestant’s turn is finished.If the an outcome is a number, the equivalent amount in dollars is won. The contestant have the right to thenstop v those winnings or can pick to rotate again, and also his or her rotate continues.If the contestant spins again and also the result is a skunk, every one of the money earned on that revolve islost and also the revolve ends.The contestant may continue adding to his or she winnings until he or she chooses to protect against oruntil a spin outcomes in a skunk.(a) What is the probability that the an outcome will it is in a number on every one of the an initial three spins of the wheel?(b) expect a contestant has actually earned $800 ~ above his or her first three spins and also chooses come spin the wheelagain. What is the intended value of his or her total winnings for the 4 spins?OR(c) A contestant who shed at this video game alleges the the wheel is not fair. In order to examine on thefairness that the wheel, the data in the table below were collected for 100 spins of this wheel.ResultFrequencySkunk33$10021$20020$50026Based on these data, can you conclude the the 4 outcomes top top this wheel room not equally likely?Give appropriate statistical evidence to support your answer.