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)= 10.4 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 = 0.01, conduct the appropriate hypothesis test

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

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

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

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

Part E Reject H0 if: State the rejection criteria for the null hypothesis for the given level of α. OS3180 Probability and Statistics Final Exam Quarter 3 AY19 9

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

Part 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”)

Part 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:-

A) The mean dwell time of a new type of UAV.

B)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 10
C)

Alternative hypothesis: u > 10

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.223607
DF = n - 1

D.F = 4

(D)

t = (x - u) / SE

t = 1.789

E)

Rejection region is p-value < 0.05.

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.789.

Thus the P-value in this analysis is 0.074.

(G)

Interpret results. Since the P-value (0.074) is greater than the significance level (0.01), we failed to reject the null hypothesis.

(H) From the above test we do not have sufficient evidence in the favor of the claim that the mean dwell time is greater than 10 hours.