Question

The management of White Industries is considering a new method of
assembling its golf cart. The present method requires 21.2 minutes, on the
average, to assemble a cart with the sample standard deviation of 1.4
minutes. Using the new method, the mean assembly time for a random
sample of 24 carts, was 20.3 minutes.

Using the 0.10 level of significance, can we conclude that the assembly time
using the new method is faster?

Answer 1

let me first rephrase the question as i think you have misquoted the information.

The management of White Industries is considering a new method of assembling it's golf cart. The present method requires 21.2 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 20.3 minutes, and the standard deviation of the sample was 1.4 minutes. Using the 0.10 level of significance,can we conclude that the assembly time using the new method is faster?

solution:

Let the population mean assemble time of golf cart be μ.

Step 1

H0: μ > 21.2 (counter claim)

H1: μ < 21.2 (claim that new method is faster)

This is a one-tailed & one sample t test.

Step 2

Write down the data you have,

The sample mean (x̄) = 20.3

The population mean (μ) = 21.2

The sample standard deviation(s) = 1.4

Number of observations (n) = 24

Standard error = SE = s /sqrt (n) = 1.4 /sqrt (24) = 0.28577

Step 3

Test statistic = (x̄ - μ) / SE = (20.3 - 21.2) / 0.28577 = - 3.15

Assume ALPHA Level = 10% = 0.1 and DF = n-1 = 24 - 1 = 23

Step 4

Critical value = -1.319 (left tailed test)

decision rule: if calculated t value is greater than this critical value (in magnitude) then we reject the null hypothesis.

and since calculated t score = 3.15(absolute value) which is greater than the critical value and fall within rejection region. So, we must reject the null hypothesis.

Also, p value = 0.002241 for DF = 23 and alpha = 0.10 from t table.

Since it is less than alpha = 0.10 hence, we again reject the null hypothesis.

hence we can conclude that is there is sufficient evidence to accept the claim that new method is faster.