Confidence Interval Calculator
Kumanga confidence mtunda kwa malire kuchokera sample malire, SD ndi kukula.
Zithunzizi zimasintha monga momwe mumalemba.
Zachidule
A confidence interval gives a range that is likely to contain the true population mean, estimated from a sample. Instead of a single best guess it reports a band together with a confidence level that says how often such bands capture the true value.
This calculator uses the z-interval: mean ± z*·(σ / √n), where z* is the standard-normal critical value for your chosen confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%) and σ / √n is the standard error. It reports the bounds, the margin of error and the standard error, and a table shows the interval at the 90%, 95% and 99% levels so you can see how the range widens as you demand more confidence.
Worked example: a sample mean of 100 with a standard deviation of 15 and 50 observations has a standard error of 15 ÷ √50 ≈ 2.12. At 95% confidence the margin is 1.96 × 2.12 ≈ 4.16, giving an interval of about 95.84 to 104.16. The z-interval suits large samples (roughly n ≥ 30) or a known population standard deviation; for small samples use a t-interval instead.
Mafunso ofunsidwa nthawi zambiri
Kodi 95% confidence interval zikutanthauza chiyani?
Izi zikutanthauza kuti ngati inu anachitanso sampling nthawi zambiri ndi anamanga mtunda nthawi iliyonse, za 95% ya iwo mtunda adzaphatikizapo anthu weniweni mwamsanga. Izi sizikutanthauza kuti pali 95% mwayi mtunda ndi m'munsimu mtunda wina.
Kodi ndiyenera kugwiritsa ntchito t-mphindi m'malo mwake?
Kugwiritsa ntchito t-nthawi yapakati pamene mzere ndi wamkulu (kuzungulira pansi 30) ndi standard deviation anthu si wodziwika. The t-kugawa ali ndi heavyer tails, kupereka pang'onopang'ono waukulu, zambiri kusamala nthawi yapakati kuposa z-kugwirizana imodzi.
Kodi ndi chiyani chimango cha vuto mu confidence mphindi?
Kusintha kwa malire ndi kutalika kwa theka la mtunda, z * · (σ / √n). Mumawonjezera ndi kuchotsa izi kuchokera ku chitsanzo choyenera kuti mupeze malire a pamwamba ndi pansi, choncho malire ang'onoang'ono amatanthauza kuwerengetsa koyenera.
Kodi ndingatani kuti ndipange mtunda wa confidence wocheperako?
Kusonkhanitsa chitsanzo chachikulu, chifukwa kutalika kumachepetsedwa ndi square root ya n, kapena kuvomereza pansi confidence level. Kuchepetsa kusinthasintha mu deta yanunso kumaletsa pakati. Kukula kwa chitsanzo kwa 4x kumachepetsa kutalika kwa pafupifupi theka.
Kodi mfundo yolimba kwambiri imachititsa kuti mtunda ukhale wochuluka?
Yes. Kufuna zambiri kukhulupilira amagwiritsa ntchito lalikulu zofunika mtengo z *, kotero 99% pakati ndi waukulu kuposa 95% pakati anamanga kuchokera pamodzi deta. Palibe nthawi zonse trade-off pakati kukhulupilira ndi precision.
Kodi ndi chiyani standard error?
Standard error is the standard deviation divided by the square root of the sample size (σ / √n). It measures how much the sample mean itself would vary from sample to sample, and it is the building block of the margin of error.
API — kugwiritsa ntchito izi calculator kuchokera code
Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Chomweko chilichonse chimene mumasiya chimagwiritsa ntchito mfundo yoyamba yomweyi yomwe tsambali limagwiritsa ntchito; mfundo yosadziwika ndi 400, siyiyenera kukhala zero yosadziwika. Onani zonse API docs →
Chithunzi
GET https://calculator.free/api/v1/confidence-interval/curl
curl "https://calculator.free/api/v1/confidence-interval/?mean=100&sd=15&n=50&conf=1.96"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/confidence-interval/?" + new URLSearchParams({
"mean": "100",
"sd": "15",
"n": "50",
"conf": "1.96"
}));
const data = await r.json();
console.log(data.results);Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.