Does the data need to be normally distributed for a t-test to work?

A researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas others received the standard amount. Would you perform a t-test of independent means or a t-test of dependent means?

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,056 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,056 lb42=168 lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 178.3 lb and a standard deviation of 36.8.

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A least squares line for a sample with 11 observations has an SSE = 192; calculate and s. Please show your work So i can understand how you arrived at the answer

A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.

A sociologist of education wants to prove that students’ sense of mastery and control before a math test could increase if students had a chance to practice with examples of questions from typical tests. The sociologist has long studied sense of content’s mastery and emotional control pre-math test with a scale called NoStressM, which ranges from 0 to 50, where 0 indicates great stress, and 50 indicates great control and mastery. In the typical student population, the day before the math test, students score 20 points on average, with a standard deviation of 6 points. The sociologist selected at a random a sample of 60 students from different schools and 3 offered them to practice for a week with questions drawn from typical math tests. The day before the math test, she administered the NoStressM scale to the 60 students and found a sample mean of 23 and a standard deviation like the one in the population. Your turn: a) Formulate the null and the alternative hypotheses that fit this…

The effectiveness of surgery for weight loss reported here found that "The surgery was associated with significantly greater weight loss [than the control group who dieted] through 2 years (61.3 versus 11.2 pounds, P<0.001)." What test could have been used and how would it have been computed?

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 43 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,009 lb.  The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,009 lb / 43 =163 lb.  What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 182.4 lb and a standard deviation of 38.4.

Assume that a high school principal believes that high number of absences hinders the students' ability to perform on standardized tests. He randomly selects a sample of 9 students who had 5 or more absences in the school year. The average ACT Composite score for this sample is X = 19 with s = 4.9. ACT Composite scores are normally distributed with u = 21.0. Do the data support the claim that the high number of absences hinders the students' ability to perform on standardized tests, using a = .05? Please show the four-step hypothesis test. %3D