Question

The makers of a child's swing set claim that the average assembly time is less than 2 hours. A sample of 35 assembly times (in hours) for this swing set is given in the table below. Test their claim at the 0.10 significance level. (a) What type of test is this? This is a right-tailed test. This is a two-tailed test. This is a left-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t x = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (e) Choose the appropriate concluding statement. The data supports the claim that the mean assembly time is less than 2 hours. There is not enough data to support the claim that the mean assembly time is less than 2 hours. We reject the claim that the mean assembly time is less than 2 hours. We have proven that that the mean assembly time is less than 2 hours. DATA ( n = 35 ) Assembly Time Hours 1.00 2.51 1.31 1.98 1.93 2.25 0.94 2.10 1.27 2.71 3.18 1.76 1.50 2.75 0.77 0.63 2.31 0.11 1.31 1.92 2.40 2.04 1.53 0.76 1.04 2.37 2.38 1.35 3.55 1.29 1.68 2.23 0.64 2.34 2.41

Answer 1

Solution: (a) This is a left-tailed test, since we are to test whether the average assembly time is less than 2 hours.

For the given problem we construct the null and alternative hypotheses as:

H0: mu = 2 vs Ha: mu < 2 [Since the claim was that, the averge time is less than 2 hours]. mu = unknown true value of the parameter

(b) The test statistic is T= (xbar-mu0)/(s/sqrt(n)) ; where xbar = sample mean, mu0 = the hypothesized value of the population mean, n = sample size, s = sample standard deviation, sqrt refers to the square root function. Under H0, T ~ t(n-1)

Here mu0 = 2, n = 35, xbar = 1.778571, sd = 0.7821958

Here, test statistic = T(observed) = -1.67 (rounded to 2 decimal places)

(c) The p-value is the probability of finding a value more extreme than the obtained test statistic assuming the null hypothesis is true. The p-value is found to be = 0.0516 (rounded to 4 decimal places)

We reject H0 if T(observed) < - t(alpha,(n-1)), where t(alpha,(n-1)) is the upper alpha point of the t - distribution with (n-1) degrees of freedom.   alpha = level of significance

or if p-value for the test statistic is less than the level of significance.

Here p-value is = 0.0516 < 0.10 and -t(alpha,(n-1)) = -1.306952(Obtained from the probability table of Student's t distribution)
Hence, T(observed) < -t(alpha,(n-1)).

(d) So we reject H0.

(e) We conclude at a 10% level of significance on the basis of the given sample that there is enough evidence to support the claim that the mean assembly time is less than 2 hours.