Confidence interval for one sample, unknown variance

Use the built-in t.test() function to calculate both the t-statistic and confidence interval automatically:

# Example dataset
data <- c(12, 15, 14, 10, 13, 16, 11, 14)

# One-Sample t-Test with 95% Confidence Interval
t.test(data, mu = 10, conf.level = 0.95)

Use scipy.stats to compute the t-test and confidence interval:

import numpy as np
import scipy.stats as stats

data = np.array([12, 15, 14, 10, 13, 16, 11, 14])

# One-Sample t-test
t_stat, p_val = stats.ttest_1samp(data, popmean=10)

# 95% Confidence Interval
mean = np.mean(data)
sem = stats.sem(data)
ci = stats.t.interval(0.95, df=len(data)-1, loc=mean, scale=sem)

print(f"t-statistic: {t_stat:.4f}")
print(f"95% Confidence Interval: {ci}")

Menu: Analyze → Compare Means → One-Sample T Test... (Set Test Value and adjust Options → Confidence Interval).

Syntax:

T-TEST
  /TESTVAL=10
  /MISSING=ANALYSIS
  /VARIABLES=score
  /CRITERIA=CI(.95).

Menu: Analyses → T-Tests → One Sample T-Test. Move your variable to Variables, set Test value under Hypothesis, and check Mean difference & Confidence interval (95%) under Additional Statistics.

Menu: Analyze → Distribution → Select Column. Click the red triangle next to your variable name → select Test Mean → enter hypothesized mean.

Run the ttest command in the command window:

ttest score == 10, level(95)

Use PROC TTEST:

proc ttest data=my_data h0=10 alpha=0.05;
   var score;
run;

Menu: Stat → Basic Statistics → 1-Sample t... Select column, check Perform hypothesis test, enter Hypothesized mean, and set confidence level under Options.

Create a Column table → Click Analyze → Select One sample t and Wilcoxon test → Enter hypothetical mean.

Calculate the margin of error using CONFIDENCE.T:

=CONFIDENCE.T(0.05, STDEV.S(A1:A10), COUNT(A1:A10))

Subtract and add this value to AVERAGE(A1:A10) to get the lower and upper bounds.