T-Test Problems A researcher wishes to determine ifa particular drug affects pilot reaction time to air traffic controller instructions. The researcher has 10 pilots. The pilots are observed in normal performance and their reaction times are recorded. Then the pilots are administered the drug, observed again, and their reaction times are recorded. The expectation is that the drug will reduce reaction time. 1. Trial 1 Time (sec) Pilot Trail 2 Time (sec) A .83 B 74 .71 C .82 .79 D 86 .87 66 F 63 G .81 .67 77 73 71 69 J .65 Conduct a t test using the five-step hypothesis testing process and StatCrunch. Show your work 2. A researcher wishes to determine if the college students with a "B" average have attain more flying hours by the end of their first semester of college than those that do not have a "B" average at the end of the first semester. The researcher surveys 20 college students that are also student pilots and records their flight hours as well as their GPA (noted as "below B" and "B or better), and, fortunately, there is an equal number "below B" and "B or better." The expectation is that those students with a B average or better will have more flying hours by the end of their first semester than those students that are below a "B" average. Here are the survey results: B or Better flying hours 52 Below B flying hours 43 32 41 44 31 36 39 37 58 51 30 44 36 55 41 62 45 52 41 Conduct a t test using the five-step hypothesis testing process and StatCrunch. Show your work. 602O8852 8

Step-by-step explanation:

Hello!

1) To test if a particular drug affects pilot reaction time to air traffic controller instruction.

The researcher sampled 10 pilots, first he recorded their normal performance and then the pilots were administered the drug and their reaction times were taken again.

The objective is to prove if the drug reduces the reaction time. There was only one sample taken and to every experimental unit (pilot) the reaction time before and after taking the drug was measured generating a paired sample data set, i.e. for each experimental unit there is a pair of values recorded. The statistic to use to test this claim is a paired sample t-test.

There are two variables of interest:

X₁: reaction time to air traffic control instructions of one pilot before taking the drug. (sec)

X₂: reaction time to air traffic control instructions of one pilot after taking the drug. (sec)

Since the variables are dependent you have to determine another one, usually referred to as "variable difference"

Xd: Difference between the reaction time to air traffic control instructions of a pilot before and after taking the drug. (X₁-X₂)

I've done a quick normality test, with a p-value 0.2303 against α: 0.05 the variable has a normal distribution so: Xd~N(μd;σd²)

If the drug does reduce the reaction time of the pilots, then the observations after taking it should be less than the observations before taking it and their differences positive, symbolically μd>0

Then the statistical hypotheses are:

H₀: μd ≤ 0

H₁: μd > 0

α: 0.05

p-value:

P(t₉≥2.11)= 1 - P(t₉<2.11)= 1 - 0.9682= 0.0318

This test and it's p-value are one-tailed to the right (remember, the p-value always has the same direction as the test) The p-value is less than the significance level, so the decision is to reject the null hypothesis.

Then you can conclude with a level of 5% that the population average of the difference between the reaction time to air traffic control instructions of the pilots before and after they took the drug is greater than zero, I .e. the drug reduces the reaction time.

2)

The researcher's objective is to compare the flying hours of two groups of pilot students.

Group 1 represents the flying hours of pilot students that have at least a "B" average GPA.

Group 2 represents the flying hours of pilot students that have less than "B" average GPA

In this exercise the researcher took two samples of students, differentiated by their GPA score, and recorded their flying hours, these two groups determine two independent study variables:

X₁: Flying hours of a pilot student with a GPA score of at least "B"

X₂: Flying hours of a pilot student with GPA score below "B"

Using the data I've run a normality test:

X₁: p-value: 0.3448 vs. α: 0.05 ⇒ X₁~N(μ₁;σ₁²)

X₂: p-value: 0.8083 vs. α: 0.05 ⇒ X₂~N(μ₂;σ₂²)

Population variances are unknown and different.

To test the hypothesis that those students with a score equal or above "B" will have more flying hours than those students with a score below B you have to apply a pooled t-test for two independent variables.

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

α: 0.05

p-value: 0.0137

The p-value is less than α, the decision is to reject the null hypothesis.

At a 5% significance level, you can say that the average flying hours of pilot students with a GPA score of at least "B" is greater than the average flying hours of the pilot students with a GPA score of less than B.

I hope it helps!

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)