A sample of size n=16 is drawn from a normally distributed population with E(X)=20 and SD(X)=8. Find (a) P(X > 24) (b) P(16 < X < 24) 0.06 Population 0.05 0.04 N(20,8) 0.03 0.02 0.01 4 08 56 10.4 15.2 20 24.8 29.6 34.4 39.2 44 X
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- If X1, X2, and X3 constitute a random sample of sizen = 3 from a normal population with the mean μ and thevariance σ2, find the efficiency of X1 + 2X2 + X34relative toX1 + X2 + X33as estimates of μ.A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 22 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 24 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is: nn x¯x¯ ss Treatment group (new drug) 22 23.48 8.01 Control group (old drug) 24 18.52 7.15 Without using software, how would you estimate the number of degrees of freedom for this problem? Select one: use the larger value, 23, chosen from the two options 21 and 23 use the smaller value, 22, chosen from the two options 22 and 24 use the larger value, 24, chosen from the two options 22 and 24 use the smaller value, 21, chosen from the two options 21 and 23IfX1 andX2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean μ and the variance σ ^2 , show that the variance of the unbiased estimator ω·Xbar1+(1−ω)·Xbar2is a minimum whenω=n1/(n1+n2)
- A sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 81 75 52 79 77 34 40 87 64 39 32 72 47 43 61 58 57 47 48 46 80 43 38 63 The hypotheses for this ANOVA test would be: H0:μA=μB=μC=μDH0:μA=μB=μC=μD HA:HA: At least one mean is different. (claim) α=0.05α=0.05 Complete the ANOVA table below: (round answers to 3 decimal places) SS df MS F p-value Between Within The decision of the test is to: reject H0H0 do not reject H0H0 The final conclusion is: There is not enough evidence to reject the claim that…Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 27 clam shells in March. 15 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. The point estimate for the true difference in proportion of dark growth bands between February and March is:Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 27 clam shells in March. 15 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. Let ? = 0.01. A) The point estimate for the true difference in proportion of dark growth bands between February and March is:
- Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 27 clam shells in March. 15 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. Let ? = 0.01.Note: Do all calculations as February - March A) The point estimate for the true difference in proportion of dark growth bands between February and March is: I need help and webassign rejected the 0.0037 as the answer. I'm so lost. I emailed my professor and he hasn't gotten back to me. Please help. Thank you.On average, a sample of n = 36 scores from a normal population with σ= 10 will provide a better estimate of the population mean than a researcher would get with a sample of n = 9 scores from a normal population with σ= 10.The management of the Seaside Golf Club regularly monitors the golfers on its course for speed of play. Suppose a random sample of golfers was taken in 2005 and another random sample of golfers was selected in 2006. The results of the two samples are as follows: 2005 2006 x1= 225 x2= 219 s1= 20.25 s2= 21.70 n1= 36 n2= 31 Based on the sample results, can the management of the Seaside Golf Course conclude that the average speed of play was different in 2006 than in 2005? Conduct the appropriate hypothesis test at the 0.10 level of significance. Assume that the management of the club is willing to accept the assumption that the populations of playing times for each year are approximately normally distributed.
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