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 n= 5 UAVs (all of the new type) resulting in a sample mean dwell time of y-bar= 9.4 ℎours. 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 s= 0.5 ℎours, and using a significance level of alpha = 0.02, conduct the appropriate hypothesis test. Formal hypothesis test conclusions.

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

2.Null hypothesis, H0: State the null hypothesis, H0 in terms of the parameter of interest H0:

3.Alternative hypothesis, H1: Specify an appropriate alternative hypothesis, H1. H1:

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

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

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

7.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”)

8.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

Given that

n=5

1) Here since we have to test the average value the parameter of interest is

2) The null hypothesis is that the population mean is 10.

3) The alternative hypothesis is that the population mean is greater than 10

4) Since the sample size is small and the population standard deviation is unknown we can use t test

5) Since the alternative is one sided the critical region is

6)

Now the critical value(tables value) of t for n-1=5-1=4 degrees of freedom and level of significance =0.02 , is

The p value is given as p=0.02

7)

which lies in the acceptance region. Hence we accept the null hypothesis and conclude that mean dwell time is 10 hours.

8) Confidence level: The level of confidence that the population parameter may be expected to lie.

Significance level: Probability of rejecting the null hypothesis H0 when it is true or P(Type I Error)

p value:The exact level of significance.or exact probability of committing Type I error

Critical value: The value of test statistic which separates the critical region and acceptance region.