# Using the Hypothesis

Test in Excel To Find

Out If Delivery Times

Have Gotten Worse

This article will explain how to use Excel to perform a Hypothesis Test to analyze delivery time for a business (a furniture store) has gotten worse. Specifically, we will show how to use Excel to perform One-Tailed, One-Sample, Unpaired Hypothesis Test of Mean to determine whether a furniture company's delivery time really has gotten worse.

This Hypothesis Test will be testing the Null Hypothesis that delivery time has not changed.

The advantages of statistical analysis in Excel to solve business statistics problems is that most problems can be solved in just one or two steps and there is no more need to look anything up on Normal Distribution tables.

Here is the problem:

**Problem: A furniture company states that its average delivery time is 15 days with a (population) standard deviation of 4 days. A random sample of 50 deliveries showed an average delivery time of 17 days. Determine within 98% certainty (0.02 significance level) whether delivery time has increased.**

Here is the Before and After data for the delivery times:

**"Before Data"**

µ = "Before Data" mean = 15

σ = "Before Data" population standard deviation = 4

**"After Data"**

xavg = "After Data" sample average = 17

n = "After Data" Sample size = 50

α = Level of Significance = 0.02

Therefore there is 2% Max chance of error.

Therefore there is a 98% Level of Certainty Required.

Before we begin solving this problem, we need to know whether we are dealing with normally distributed data. If the data is not normally distributed, we have to use nonparametric statistical tests to solve this problem.

**Always Test for Normality First**

Normality tests should be performed on the before and after delivery time data. Both data sets must be normally distributed to perform the well-known hypothesis test that is based upon the underlying data being normally distributed. This blog has numerous articles about how to perform normality testing and nonparametric testing if the data is not normally distributed.

__The MOST Important Step__

Determine What Type of Hypothesis

Determine What Type of Hypothesis

Test You Will Perform

Test You Will Perform

**1) Hypothesis Test of Mean or Proportion?**

We know that this is a

**test of mean**and not proportion because

**each individual sample taken can have a wide range of values:**Any delivery time sample measurement from 12 to 18 days is probably reasonable.

**2) One or Two-Tailed Hypothesis Test?**

We know that this is a

**one-tailed test**because we are trying to

**determine if the "After Data" mean delivery time is larger (worse) than the "Before Data"**mean delivery time, not whether the mean mean delivery time is merely different, which would be a two-tailed test.

**3) One or Two-Sample Hypothesis Test?**

We know that only

**one sample**needs to be taken because the population data being tested is already available.

**4) Paired or Unpaired Hypothesis Test?**

This is

**unpaired data**because groups are sampled independently.

In this case, we are performing a

**to determine whether a furniture store's mean delivery time has really gotten worse. We will do this test in Excel. It is extremely important to establish the type of Hypothesis test. Each type of Hypothesis test uses a slightly (or very) different methodology and set of formulas.**

__One-Tailed, One-Sample, Unpaired Hypothesis Test of Mean__**The Four-Step Method That Solves**

__ALL__Hypothesis Tests**Step 1 - Create the Null and Alternate Hypotheses**

The Null Hypothesis normally states that both means are the same.If the "Before Data" population mean, µ, equals the "After Data" sample mean, x

**avg**, then x

**avg**= µ = 15

**avg**= 15

**avg**is larger than µ (which is 15), is as follows::

**avg**is greater than 15

For this one-tailed test, the Alternative Hypothesis states that the value of the distributed variable x

**avg**is larger than the value of 15 stated in the Null Hypothesis,

**OR**is less than (Constant)

**Step 2 - Map the Normal Curve**

**avg**.

**avg**= 15, the Normal curve will map the distribution of the variable xavg with a mean of x

**avg**= 15.

**xavg**= s / SQRT(n) = 4 / SQRT(50) = 0.566

*Click On Image To See Larger Version***Step 3 - Map the Region of Certainty**

**98%**,

**1-tailed**= NORMSINV(1 - α) = NORMSINV(

**0.98**) = 2.05

*Excel Note - NORMSINV(x) = The number of standard errors from the Normal curve mean to a point right of the Normal curve mean at which x percent of the area under the Normal curve will be to the left of that point.*

*Additional note - For a one-tailed test, NORMSINV(x) can be used to calculate the number of standard errors from the Normal curve mean to the boundary of the Region of Certainty whether it is in the left or the right tail.***avg**= 15 by 2.05 standard errors.

**xavg**= 0.566, so:

**95%**,

**one-tailed*** s

**xavg**

*Click Image To See Larger Version***avg**= 15

**Step 4 - Perform Critical Value and p-Value Tests**

**a) Critical Value Test**

**avg**, falls inside or outside of the Critical Value, which is the boundary between the Region of Certainty and the Region of Uncertainty.

**avg**, falls within the Region of Certainty, the Null Hypothesis is not rejected.

**avg**, falls outside of the Region of Certainty and, therefore, into the Region of Uncertainty, the Null Hypothesis is rejected and the Alternate Hypothesis is accepted.

**avg**= 17 and is therefore to the right of (outside of) the outer right Critical Value (16.16), which is the boundary between the Regions of Certainty and Uncertainty in the right tail.

*Click On Image To See Larger Version*

b) p Value Test

b) p Value Test

**xavg**= 1 - NORMSDIST( [ x

**avg**- µ ] / s

**xavg**)

*Excel note - NORMSDIST(x) calculates the total area under the Normal curve to the LEFT of the point that is x standard errors to the right of the Normal curve mean. Since we are calculating the area to the RIGHT of this point, we use 1 - NORMSDIST..***xavg**= 1 - NORMSDIST((17 - 15 ) / 0.566) = 1 - NORMSDIST(2.0/0.566) = 0.0002

*Click Image To See Larger Version******************************************

Using the Hypothesis Test in Excel to Find Out If Your Delivery Time Has Gotten Worse

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**Excel Master Series Blog Directory**

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