Question

On your first day on the job, your boss asks you to conduct a hypothesis test about the mean dwell time of a new type of UAV. Before you arrived, an experiment was conducted on ? = 5 UAVs (all of the new type) resulting in a sample mean dwell time of ?1 = 10.4 h????. The goal is to conclusively demonstrate, if possible, that the data supports the manufacturer’s claim that the mean dwell time is greater than 10 hours. Given that it is reasonable to assume the dwell times are normally distributed, the sample standard deviation is ? = 0.5 h????, and using a significance level of ? = 0.01, conduct the appropriate hypothesis test.

Formal hypothesis test conclusions.

A) Parameter of interest: From the problem context, identify the parameter of interest.

B) Null hypothesis, H0: State the null hypothesis, H0 in terms of the parameter of interest H0:

C) Alternative hypothesis, H1: Specify an appropriate alternative hypothesis, H1. H1:

D) Test Statistic: Determine an appropriate test statistic (equation; state degrees if freedom if necessary).

E) Reject H0 if: State the rejection criteria for the null hypothesis for the given level of α.

F) Computations: Compute any necessary sample quantities, substitute these into the equations for the test statistic, and compute that value. Perform P-Value calculations.

G) Draw conclusions: Decide whether or not H0 should be rejected and report that in the problem context. Make a “real-world” statement about the outcome of the test (cannot just say “reject the null hypothesis”)

H) Provide an illustration of the hypothesis test you conducted above, making sure that you annotate: the confidence level, the significance level, the test statistic, the critical value, and the p-value.

Answer 1

Solution:

Part A

The parameter of interest for this research study is given as population mean dwell time of a new type of UAV.

Part B)

The null hypothesis for this test is given as below:

Null hypothesis: H₀: The mean dwell time of a new type of UAV is 10 hours.

H₀: µ = 10

Part C)

The alternative hypothesis for this test is given as below:

Alternative hypothesis: H_a: The mean dwell time of a new type of UAV is greater than 10 hours.

H_a: µ > 10

Part D

The test statistic formula for this test is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given information, we have

Xbar = 10.4

µ = 10

S = 0.5

n = 5

df = n – 1 = 5 – 1 = 4

α = 0.01

Critical t value = 3.7469

t = (Xbar - µ)/[S/sqrt(n)]

t = (10.4 - 10)/[0.5/sqrt(5)]

t = 0.4/ 0.2236

t = 1.7889

Test statistic = t = 1.7889

Part E

n = 5

df = n – 1 = 5 – 1 = 4

α = 0.01

Critical t value = 3.7469

So, rejection criterion is given as below:

Reject H₀ if test statistic t > 3.7469

Part F)

n = 5

df = n – 1 = 5 – 1 = 4

α = 0.01

Critical t value = 3.7469

Test statistic = t = 1.7889

So, P-value = 0.0741

(by using t-table)

Part G

P-value > α = 0.01

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the mean dwell time of a new type of UAV is greater than 10 hours.