{"id":28427,"date":"2025-06-20T12:20:44","date_gmt":"2025-06-20T12:20:44","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28427"},"modified":"2025-06-20T12:20:45","modified_gmt":"2025-06-20T12:20:45","slug":"for-a-confidence-level-of-85-find-the-critical-value","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/for-a-confidence-level-of-85-find-the-critical-value\/","title":{"rendered":"For a confidence level of 85%, find the critical value"},"content":{"rendered":"\n

For a confidence level of 85%, find the critical value<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

To find the critical value<\/strong> for a confidence level of 85%<\/strong>, we are typically referring to a z-score<\/strong> (when population standard deviation is known or large sample size) or t-score<\/strong> (when standard deviation is unknown and sample size is small). For this explanation, we will assume the standard normal distribution<\/strong> (z-distribution).<\/p>\n\n\n\n

\n\n\n\n

\u2705 Correct Answer:<\/strong><\/h3>\n\n\n\n

The critical value (z*)<\/strong> for an 85% confidence level<\/strong> is approximately:<\/p>\n\n\n\n

z* = \u00b11.44<\/strong><\/p>\n\n\n\n

\n\n\n\n

\ud83d\udcd8 Explanation (300 words):<\/strong><\/h3>\n\n\n\n

In statistics, a confidence level<\/strong> is the percentage of all possible samples that can be expected to include the true population parameter. An 85% confidence level<\/strong> means that we are 85% confident that the true population parameter lies within the confidence interval.<\/p>\n\n\n\n

To calculate the critical value<\/strong> for a confidence level using the standard normal (z) distribution<\/strong>, follow these steps:<\/p>\n\n\n\n

\n\n\n\n

Step 1: Understand the Confidence Level<\/h3>\n\n\n\n

An 85% confidence level<\/strong> means that the middle 85%<\/strong> of the normal distribution is between two z-scores, with 15%<\/strong> left in the tails (7.5% in each tail because it’s a two-tailed test).<\/p>\n\n\n\n

\n\n\n\n

Step 2: Find the Area in One Tail<\/h3>\n\n\n\n
    \n
  • Total area in both tails = 100% \u2212 85% = 15%<\/li>\n\n\n\n
  • Area in one tail = 15% \u00f7 2 = 7.5%<\/strong> = 0.075<\/strong><\/li>\n<\/ul>\n\n\n\n

    So, we are looking for the z-value<\/strong> where the area to the left<\/strong> is:<\/p>\n\n\n\n

    1 \u2212 0.075 = 0.925<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Use the Standard Normal Table or Calculator<\/h3>\n\n\n\n

    Look up the z-score that corresponds to 0.925<\/strong> cumulative area. This value is:<\/p>\n\n\n\n

    z \u2248 1.44<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Step 4: Interpret the Result<\/h3>\n\n\n\n

    Since it’s a two-tailed test, the critical values are:<\/p>\n\n\n\n

    \u00b11.44<\/strong><\/p>\n\n\n\n

    This means if you were constructing a confidence interval, you would go 1.44 standard deviations<\/strong> above and below the sample mean.<\/p>\n\n\n\n

    \n\n\n\n

    \ud83d\udd11 Summary:<\/h3>\n\n\n\n
      \n
    • Confidence level: 85%<\/strong><\/li>\n\n\n\n
    • Tails: 7.5% in each<\/li>\n\n\n\n
    • Cumulative area to left: 0.925<\/strong><\/li>\n\n\n\n
    • Critical value (z*) = \u00b11.44<\/strong><\/li>\n<\/ul>\n\n\n\n

      This critical value helps construct the confidence interval or perform hypothesis tests with 85% confidence.<\/p>\n","protected":false},"excerpt":{"rendered":"

      For a confidence level of 85%, find the critical value The correct answer and explanation is: To find the critical value for a confidence level of 85%, we are typically referring to a z-score (when population standard deviation is known or large sample size) or t-score (when standard deviation is unknown and sample size is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28427","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28427","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28427"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28427\/revisions"}],"predecessor-version":[{"id":28431,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28427\/revisions\/28431"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28427"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28427"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}