Question 3 A fruit farmer has a large number of almond trees, all of the same variety and the same age. One year he wishes to estimate the mean yield of his trees. He collects all the almonds from 8 trees and records the following weights (kg); 36 53 78 67 92 77 59 66 a) Use these data to estimate the mean and standard deviation of the yields of all the farmer's trees. b) Construct a 95% confidence interval for the mean yield. c) What statistical assumption is required for your procedure to be valid? d) How might you select a sample of eight trees from those growing in a large field.

1. Metal Tags on Penguins and Length of Foraging Trips. Data were collected over a 10-year timespan from a sample of penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. From a sample of 344 foraging trips for metal-tagged penguins, the mean length was 12.70 days. From a sample of 512 foraging trips for electronic-tagged penguins, mean length was 11.60 days. Test whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. a. State hypotheses in terms of two means. b. Calculate the sample statistic XM - XE c. An estimate of the standard error for this difference of means is SE-0.2834. Calculate a test statistic to two decimal places. d. What is the correct theoretical distribution for this test? ☐Normal ☐t with degrees of freedom e. Find the p-value and draw a…

Past records suggest that the mean annual income, µ,, of teachers in state of New York is less than or equal to the mean annual income, µ,, of teachers in Illinois. In a current study, a random sample of 15 teachers from New York and an independent random sample of 15 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows: Annual income in dollars New York 46406, 43039, 47083, 47056, 46810, 47074, 43524, 59524, 49763, 48083, 46100, 53904, 43171, 44341, 52229 Illinois 53010, 43485, 39037, 47622, 47151, 50372, 41401, 35007, 40591, 49268, 44782, 39668, 52555, 49976, 49207 The population standard deviation for mean annual income of teachers in New York and in Illinois are estimated as 6600 and 6200, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of New York is…

Grades 50-60 60-70 70-80 80-90 90-100 No. of Students 11 1 Calculate the standard deviation of the sample grouped data above. ) 13.52 ) 13.09 O 12.41 ) 12.70 2.

A. What is the 95% Cl of a population mean when the mean of a sample is 10, the standard deviation is 2, and the sample size is 100?  B. What is the 95% Cl of a population mean when the mean of a sample is 10, the standard deviation is 2, and the sample size 25? C. discuss the difference in these Cis. What is the relationship between the Cl range and sample size?

The figure shows population density (people per square mile) for all states of a certain country. The states are divided into four geographical regions: A, B, C, and D. Answer the questions below. D- 0 100 200 300 400 500 600 700 800 900 1000 1100 People per Square Mile Why is it best to compare medians and interquartile ranges for these data, rather than comparing means and standard deviations? OA. These data are fairly symmetric and do not have outliers, and the median and interquartile range provide more reliable information in these circumstances. B. Some of these data have outliers and/or are skewed, and the median and interquartile range amplify the effects of outliers and skewness. OC. Some of these data have outliers and/or are skewed, and the median and interquartile range are resistant to outliers. OD. Some of these data have vastly different centers, and the median and interquartile range provide more reliable information in these circumstances. List the approximate median…

Part C. Compute the sample mean and sample deviation.

Consider the following population data; 0, -4, 2, -8, 10 a) Calculate the population variance. b) Calculate the population standard deviation

The distribution of male height (X) in the US is known to be normally distributed with mean of about 70 inches and variance of 25 inches. What is the IQR? (hint: think about what the IQR represents in a boxplot with regard to percentiles). The z tables can be found at the bottom of the written portion of the exam or at the end of Lecture Note 10. a.) 5.0 b.) 9.0 c.) 7.3 d.) 10.0 e.) 6.7

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and a standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.1 pounds, what is the Z-score for this observation?   Question 3 options:   1)  2.500   2)  0.625   3)  -0.625   4)  1.250