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. What is the null and alternative hypotheses?

Answers

a) H_0: \mu\leq15\\\\H_1: \mu15

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:

H_0: \mu\leq15\\\\H_1: \mu15

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:

z=\frac{M-\mu}{\sigma/\sqrt{n}}=\frac{16.2-15}{5.6/\sqrt{49}}=\frac{1.2}{0.8}=1.5

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:

P(z1.5)=0.067

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.


Acarpet company advertises that it will deliver your carpet within 15 days of purchase. a sample of

Null Hypothesis

• Symbolized by Ho, which states the absence of relationships between the independent and dependent variables.

• It is therefore a statement to disprove the fact that the independent variable has an effect on the dependent variable.

Alternative Hypothesis

• Opposite of Null Hypothesis

• Symbolized by Hi

• The alternative hypothesis states the relationship between the independent and dependent variables and the fact that the first affects the second one. (Morgan, 2014; Thomas, 2013)

A null hypothesis has a key word which is "no", if used, it is stated for example: "The kind of fertilizer have no significant effect on the growth of the plant", while alternative hypothesis is stated as: "The kind of fertilizer has significant effect on the growth of the plant". Null hypothesis is negatively stated, and the commonly used, while alternative is positively stated.



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