Question

The management of gogo carts is considering a new method of assembling its golf cart. the present method requires a mean time of 42.3 minutes to assemble a cart. the mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. using the 0.10 level of significance, can we conclude that the assembly time using the new method is faster?

a. what is the decision rule? (negative amount should be indicated by a minus sign.

Answer 1

The decision rule for a one-tailed hypothesis test with a significance level of 0.10 is to reject the null hypothesis if the test statistic is less than the critical value. In this case, the critical value is -1.28.

Step-by-step explanation:

To determine if the assembly time using the new method is faster, we can perform a hypothesis test. The null hypothesis (H0) is that the mean assembly time using the new method is equal to the mean assembly time using the present method. The alternative hypothesis (Ha) is that the mean assembly time using the new method is less than the mean assembly time using the present method.

The decision rule for a one-tailed test with a significance level of 0.10 is as follows:

If the test statistic is less than the critical value (negative value), we reject the null hypothesis in favor of the alternative hypothesis. If the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.

To calculate the critical value, we need to find the z-score corresponding to a 0.10 cumulative probability in the left tail of the standard normal distribution. Using a standard normal table or calculator, we find the z-score to be approximately -1.28. Therefore, the decision rule is to reject the null hypothesis if the test statistic is less than -1.28.