Question

part 1
An independent measures study was conducted to determine whether a new medication called "Byeblue" was being tested to see if it lowered the level of depression patients experience. There were two samples, one that took ByeBlue every day and one that took a placebo every day. Each group had n = 30. What is the df value for the t-statistic in this study?
a. 60
b. 58
c. 28
d.  There is not enough information

part 2.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 3.9% or largest 3.9%.

What is the minimum head breadth that will fit the clientele?
min =

What is the maximum head breadth that will fit the clientele?
max =

Do not round your answer.

Answer 1

Solution:

Part 1) An independent measures study was conducted to determine whether a new medication called "Byeblue" was being tested to see if it lowered the level of depression patients experience.

There were two samples, one that took ByeBlue every day and one that took a placebo every day.

Each group had n = 30.

That means: ByeBlue group has sample size = n1 = 30 and Placebo group has sample size = n2 = 30

We have to find the df value for the t-statistic in this study.

Thus df = n1 + n2 - 2   = 30 + 30 - 2 = 58

Thus correct option is: b) 58

Part 2)

Given: the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 0.8-in.

That is:

Mean =    and standard deviation =

Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 3.9% or largest 3.9%.

What is the minimum head breadth that will fit the clientele?

That is: find x value such that:

P(X < x) = 3.9%

P(X < x ) =0.0390

Thus find z such that: P( Z < z ) = 0.0390

Look in z table for Area = 0.0390 and find corresponding z value.

Area 0.0392 is closest to 0.0390, and it corresponds to -1.7 and 0.06

Thus z = -1.76

Since Normal distribution is symmetric, z value for lower tail 0.0390 area is -1.76 , then z value for upper tail 0.0390 area would be +1.76

Now use following formula:

and

What is the minimum head breadth that will fit the clientele? Answer:

What is the maximum head breadth that will fit the clientele? Answer :