Question

In: Statistics and Probability

Historically, the average time it takes Jessica to swim the 200 m butterfly is 148.4 seconds....

Historically, the average time it takes Jessica to swim the 200 m butterfly is 148.4 seconds. Jessica would like to know if her average time has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds. Assume the population standard deviation is 2.2 seconds.

a) Perform the appropriate test of hypothesis to determine whether Jessicas average time has decreased. Use ↵ = 0.05.

Compute the type II error of the test if Jessicas actual mean swimming time is 147.0 seconds. Interpret the results.

i mostly need help with b. (show all your work please) ty

Solutions

Expert Solution



Related Solutions

When a machine is properly calibrated, it takes an average time of 19.0 seconds to produce...
When a machine is properly calibrated, it takes an average time of 19.0 seconds to produce a widget, with a standard deviation of 2.8 seconds. For a simple random sample of n = 36 widgets, the sample mean production time is found to be x-bar = 20.2 seconds. If the machine was properly calibrated, what is the probability that the mean for this sample would be 20.2 seconds or more? Now that you know the probability of this sample mean...
, Recording the time it takes (in seconds) for the temperature to drop in increments of...
, Recording the time it takes (in seconds) for the temperature to drop in increments of 2ºC:                               Temperature(°C)                  Time(in second)                          2ºC                  00:52.82                          2ºC                  00:53.94                          2ºC:                  00:64.48                        2ºC:                   00:67.44                          2ºC:                  00:68.34                        2ºC                  00:79.83 1, You will treat temperature as if it were a concentration (of heat). In order to analyze the data, you will need to know the difference between each temperature value recorded and the original...
Time String to Seconds Write a method that takes a string representation of time in hours:minutes:seconds...
Time String to Seconds Write a method that takes a string representation of time in hours:minutes:seconds and returns the total number of seconds For example, if the input is “0:02:20” it would return 140 If the input string is missing the hours component it should still work For example, input of “10:45” would return 645 Write an overloaded form of the method that takes in only hours and minutes and returns the total number of seconds It should leverage the...
The length of time it takes a baseball player to swing a bat (in seconds) is...
The length of time it takes a baseball player to swing a bat (in seconds) is a continuous random variable X with probability density function (p.d.f.) f(x) = ( ax + 8/9 for 0 ≤ x ≤ b (c) Calculate (to 3 decimal places of accuracy) the median of X. (d) What is the probability that the baseball player takes between 5 and 10 swings (inclusive) before a swing whose length is greater than the median in part (c) occurs...
McDonald’s makes the claim that it takes 90 seconds or less from the time a car...
McDonald’s makes the claim that it takes 90 seconds or less from the time a car stops at the order point to delivery of an order through the window. How can McDonald’s substantiate this claim when drive-thru times vary? How does McDonald’s quantify the uncertainty surrounding its estimate of drive-thru service time? How can the variability in drive-thru service times be quantified? Why is it important to understand variability? Why is it important for McDonald’s to effectively communicate its statistical...
A) What is the rate constant for the reaction with an average time of 48.6 seconds,...
A) What is the rate constant for the reaction with an average time of 48.6 seconds, between 3.00 ml of 0.1 M t-butyl chloride, 3 ml 0.01 M NaOH, 4 ml water with 3 drops bromophenyl blue solution. B) What is the rate constant for the reaction with an average time of 48.6 seconds, between 3.00 ml of 0.1 M t-butyl chloride, 6 ml 0.01 M NaOH, 1 ml water with 3 drops bromophenyl blue solution.
1) The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What...
1) The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes? A) 0.4706 B) 0.5294 C) 0.6000 D) 0.7059 2) For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to ________. A) 68% B) 68.26% C) 95% D) 99.73% 3) Which of the following...
When boiling​ water, a hot plate takes an average of 7 minutes​ [min] and 25 seconds​...
When boiling​ water, a hot plate takes an average of 7 minutes​ [min] and 25 seconds​ [s] to boil 150 milliliters​ [mL] of water. Assume the temperature in the lab is 72 degrees Fahrenheit ​[Superscript o Baseline Upper F​]. The hot plate is rated to provide 592 watts​ [W]. If we wish to boil 150 milliliters​ [mL] of acetone using this same hot​ plate, how long do we expect the process to​ take? Acetone has a boiling point of 56...
A professional baseball pitcher takes 14.76 seconds to throw each pitch, on average. Assume the pitcher's...
A professional baseball pitcher takes 14.76 seconds to throw each pitch, on average. Assume the pitcher's times per pitch follow the normal probability distribution with a standard deviation of 2.2 seconds. Complete parts a through c. a). What is the probability that a random sample of 10 pitches from this pitcher will have a mean less than 14 seconds? P(x< 14) = b). What is the probability that a random sample of 30 pitches from this pitcher will have a...
When boiling​ water, a hot plate takes an average of 88 minutes​ [min] and 1515 seconds​...
When boiling​ water, a hot plate takes an average of 88 minutes​ [min] and 1515 seconds​ [s] to boil 170170 milliliters​ [mL] of water. Assume the temperature in the lab is 6969 degrees Fahrenheit. The hot plate is rated to provide 501501 watts​ [W]. If we wish to boil 170170 milliliters​ [mL] of acetone using this same hot​ plate, how long do we expect the process to​ take? Acetone has a boiling point of 5656 degrees Celsius. ​[Hint: you must...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT