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Title screen: Conducting a one-sample z test of the mean. Copyright ©2017 McGraw-Hill Education. All rights reserved.
Narrator: "This video demonstrates how to conduct a one-sample test of a hypothesis about a population mean when the population standard deviation is known. An airport manager has to decide whether to expand the space available for short-term parking at a small regional airport. If average parking time is more than 40 minutes, he can justify expanding the lot. Several years of data indicate the parking time has a standard deviation of 10 minutes. Lately, customers have complained that it is difficult to find space in the lot, and the manager believes the parking time has increased. He has randomly selected a sample of 12 cars' parking time, shown in this file. Excel doesn't have a hypothesis test specific to a one-sample test of the mean, but we are going to adapt the two-sample z-test to our needs. First, I'll set up a dummy variable in column 'B.' And I've entered a 0 so there is a value in this column."
Dummy is entered into cell B1, zero is entered into B2.
Narrator: "Then I'll go to Data, Data Analysis, and I'll go all the way down to the z-test to sample for means."
Data Analysis is found in the Analysis section of the Data tab. The dialog box appears when clicked, which contains a list of Analysis Tools. z-Test: Two Sample for Means is selected from the box, which opens a new dialog box.
Narrator: "My Variable1 range is the sample data. I'm going to include the column header. My Variable2 range is the dummy and the 0. Let's consider what our null and alternative hypothesis are. The null hypothesis is that parking time is less than or equal to 40 minutes. The alternative hypothesis is that parking time is greater than 40 minutes."
Text: H0: mu less than or equal to 40 minutes. HA or H1: mu greater than 40 minutes.
Narrator: "Therefore, the hypothesized mean difference is 40 minutes—what the mean is that we are testing. Variable1's variance—notice that it says 'Known.' Because we're using a z-test here, we know the population standard deviation."
Text: Sigma is 10 minutes. Ten squared equals 100, the variance.
Narrator: "For Variable1, we are going to enter the variants for the population—100. Remember that we are adapting a two-sample test to a one-sample test. We don't have a second variable's variance. But we cannot enter a 0 because Excel will not allow that, so we're gonna enter a value as close to 0 as we can so that it won't affect our final results. I click to select Labels. My alpha is . 05. I'll have my output in this tab. And now I'm ready to click 'Okay.'"
Within the z-Test dialog box, Variable 1 Range is set to $A$1:$A$13, Variable 2 Range is set to $B$1:$B$2, Hypothesized Mean Difference is set to 40, Variable 1 Variance (known) is set to 100, Variable 2 Variance (known) is set to 0.001, the Labels checkbox is checked, Alpha is left at its default 0.05, and the Output Range radio button is selected to enter $D$1 into its text field. When OK is clicked, a z-Test table appears in the sheet.
Narrator: "I'll expand the results so we can see everything. You can see this dummy column here. We don't need this column. We're also able to change this from a z-test for two sample to one sample. "
The dummy data in column F is deleted. The table title in cell D1 is edited to z-Test: One Sample for Means. Text: Let's clean up our output so that it is appropriate to a one sample test for the mean.
Narrator: "And here it's the hypothesized mean, not the hypothesized mean difference. Now we have our output for a one-sample test. The mean of our sample is 48 minutes. The known variance of 100, Excel has taken the square root of that and divided it by the square root of 12 in order to determine standard error, which was then used to calculate the 'Z.'"
The formula entered into cell F8: equals left parenthesis 48 minus 40 right parenthesis divided by left parenthesis 10 divided by s q r t left parenthesis 12 right parenthesis right parenthesis.
Narrator: "If we take 48 minus 40, divided by 10 over the square root of 12, we get the 2. 77. This is how Excel has calculated the test statistic. We're using a one-tailed test because we are testing the alternative hypothesis that 'mu' is greater than 40 minutes."
An arrow points to cell E10.
Narrator: "Our 'P' value is quite a bit smaller than our alpha of . 05. When 'P' value is less than alpha, we reject the null hypothesis."
An arrow points to cell E9.
Narrator: "This is the 'Z' value that you would look up in the standard normal table, based on a significance level of 5%, and compare it with the test statistic of 2. 77."
The Z value in cells D and E10 is compared to the Z value in cells D and E8.
Narrator: "If the test statistic is greater than the 'Z' critical value, again we would reject the null hypothesis. Either way, whether we use the 'P' value or the 'Z' score, we would reject the null hypothesis. This video demonstrated how to use Excel's data analysis two-sample z-test to conduct a one-sample z-test when population standard deviation is known."
Video has ended.
Described transcript ©2023 McGraw Hill. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.
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