A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days. a. State the null and alternative hypotheses.
b. Using a critical value, test the null hypothesis at the 5% level of significance.
c. Using a p-value, test the hypothesis at the 5% level of significance.
d. What type of error may have been committed for this hypothesis test
Answers
Answer:
a)
b) The z-value (1.5) is smaller than z=1.645 (critical value), so it is in the "acceptance region". It failed to reject the null hypothesis.
c) The p-value (0.07) is greater than the significance level (0.05), so it failed to reject the null hypothesis.
d) In this case, the error we may hae comitted is a Type II error (failed to reject a null hypothesis that is false).
Step-by-step explanation:
We have to perfomr a hypothesis test on the mean, with known standard deviation of the population.
a) The null hypothesis is that the deliver time is 15 days or less.
The null and alternative hypothesis are then:
The significance level is defined as 0.05.
b) The critical value of z for a one-side test (rigth side) and a significance level of 0.05 is z=1.645.
If the z-value for this sample is higher than 1.645, it is in the "rejection region".
Calculating the z-value:
The z-value (1.5) is smaller than z=1.645 (critical value), so it is in the "acceptance region". It failed to reject the null hypothesis.
c) The p-value for z=1.5 is:
The p-value (0.07) is greater than the significance level (0.05), so it failed to reject the null hypothesis.
d) There are two types of error:
Type I errors: happen when we reject a null hypothesis that is true.
Type II errors: happen when we failed to reject a null hypothesis that is false.
In this case, the error we may hae comitted is a Type II error.
The null hypothesis at 5% significance level is 1.50
Data;
- n = 49
- mean = 16.2
- standard deviation = 5.6
Null and Alternative Hypothesis
The alternative hypothesis are
H_o = mean = 15
standard deviation = 5.6 days
using z-test,
n is greater than or equal to 30
Assuming standard deviation is known
z-critical value is 1.96 at 95% confidence level.
Since z-critical value is greater than the test statistic, so we tail to subject H_o.
There's no evidence that mean delivery time is different from 15 days.
Learn more on hypothesis here;
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