ONE-SAMPLE HYPOTHESIS TEST OF MEANS.

January 22, 2026

An image of the SPSS Histogram (Sample Data - Consumer Spending)

SPSS Histogram - A random sample of consumer spending.

Depending on the p-value, we reject or fail to reject the null hypothesis (H₀). If p-value < the significance level, we reject H₀.

Hypothesis testing compares a sample mean to the population mean—a theoretical, an existing level, a rate, or a standard—to reject the null hypothesis.

In the following example, the company wants to find out the evidence to support the claim that the average consumer spending < $380 in a typical month.

Example 12

A large retail company has a chain of stores. The chain store sales, given in the following table, represent a random sample of consumer spending in a typical month. Based on the hypothetical data given in the table, see if there is evidence that the average amount spent on groceries is less than $380. Use α= 0.05. Assume that the survey data collected by the store chain follow a normal distribution.

Case	Store ID	Customer ID	Amount Spent ($)
1	1	2	383
2	2	21	341
3	8	142	265
4	9	162	359
5	15	285	537
6	17	323	311
7	19	364	511
8	21	402	225
9	21	403	379
10	25	485	227
11	25	487	386
12	25	488	358
13	26	501	253
14	26	504	555
15	27	521	322
16	27	522	530
17	32	622	412
18	36	702	382
19	37	729	366
20	38	742	345
21	39	762	292
22	42	821	487
23	43	846	579
24	53	1044	403
25	54	1061	343
26	54	1062	289
27	54	1066	367
28	56	1106	202
29	59	1161	386

When we selected an α = 0.05 (or 95% confidence), we are accepting a 5% chance of being wrong (type I error).

Create the variables (StoreID, CustID, and Amount) directly in the variable view, and input the sample data into the data view.

	Name	Type	Values	Missing	Measure
1	StoreID	Numeric	None	None	Nominal
2	CustID	Numeric	None	None	Nominal
3	Amount	Numeric	None	None	Scale

H₀: The NULL hypothesis (States “No difference”)
H₁: The ALTERNATIVE (or research) hypothesis (States “There is a difference”)

TWO-TAILED TEST

H₀: µ = $380 Mean monthly grocery spending per consumer
H₁: µ ≠ $380 Mean monthly grocery spending per consumer

Run One-Sample T test…

Analyze → Compare Means → One-Sample T Test…

SPSS One-Sample T Test Inputs.

Move the variable (Amount) into the “Test Variable(s)” box
Options: Change Confidence Interval percentage (95%, 99% ..)—CI
Input the value (380) into the “Test Value” box
Run the test (OK)
Output: “Sig. (2-tailed)” is the P-value for two-sided test

The p value (0.681) is greater than 5% so we fail to reject the null hypothesis.

SPSS One-Sample T Test Output.

ONE-TAILED TEST

H₀: µ = $380 Mean monthly grocery spending per consumer
H₁: µ < $380 Mean monthly grocery spending per consumer

Run One-Sample T test…

Analyze → Compare Means → One-Sample T Test…

Move the variable (Amount) into the “Test Variable(s)” box
Options: Change Confidence Interval percentage (95%, 99% ..)—CI
Input the value (380) into the “Test Value” box
Run the test (OK)
Output: “Sig. (2-tailed)” is the P-value for two-sided test.

The one-sided T Test, p-value should be (Sig. 2-tailed)/2. Therefore, one-sided T Test, p-value (0.3405) is greater than 5%. So, we also fail to reject the null hypothesis with one-sided T Test.

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ONE-SAMPLE HYPOTHESIS TEST OF MEANS.