Academic managers online nowFree quote in 3 minutes. Assignments from $19.Submit assignment →
Free, no account, nothing storedThe arithmetic runs in your browser. Nothing you type is sent to us.All 100 calculators →

Statistics & Data Science · pattern F, Dataset

A one-sample z test, stated properly.

Enter a sample mean, hypothesised mean, standard deviation and sample size for the test statistic, the p-value and a conclusion phrased the way a marker expects to read it.

Inputs

The formula used

z = (x̄ − μ₀) ÷ (s ÷ √n)

A one-sample test of a mean against a hypothesised value, assuming the sampling distribution of the mean is approximately normal — reasonable above about thirty observations.

Test statistic z

2.3373

Standard error
1.45465
Difference from μ₀
3.4000
Two-tailed p-value
0.01942
Decision
reject the null hypothesis at this α
Effect size, Cohen's d
0.3696
95% interval for the mean
65.549 to 71.251

Failing to reject the null is not evidence that the null is true. It means this sample did not provide enough evidence against it, which is a different and weaker statement.

Write the conclusion in the language of evidence.

The correct phrasing is that the null hypothesis is rejected or not rejected at a stated significance level, never that it is proved or disproved. Marks are routinely lost for writing that a test proves the alternative. State the hypotheses, the statistic, the p-value, the decision and the effect size — in that order — and the presentation criteria look after themselves.

Questions about hypothesis test

z test or t test?
Use t when the population standard deviation is unknown and n is small, which is most coursework. Above about thirty observations the two agree closely.
What is a Type I error?
Rejecting a true null hypothesis — a false positive. Its probability is α. A Type II error is failing to reject a false null, and its probability falls as sample size rises.
Can I test more than one hypothesis on the same data?
Only with a correction such as Bonferroni. Twenty independent tests at α = 0.05 produce one significant result by chance on average.

A calculator handles the arithmetic. It cannot teach you the method.

If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.

Statistical output here is for coursework and learning. Reported p-values and intervals assume the conditions stated on the page; nothing here checks whether those conditions hold for your data.