{"id":70,"date":"2021-01-12T22:19:39","date_gmt":"2021-01-12T22:19:39","guid":{"rendered":"https:\/\/textbooks.jaykesler.net\/introstats\/part\/hypothesis-testing-with-one-sample\/"},"modified":"2023-04-19T19:18:36","modified_gmt":"2023-04-19T19:18:36","slug":"hypothesis-testing-with-one-sample","status":"publish","type":"part","link":"https:\/\/textbooks.jaykesler.net\/introstats\/part\/hypothesis-testing-with-one-sample\/","title":{"rendered":"Hypothesis Testing with One Sample"},"content":{"raw":"\r\n[latexpage]\r\n<\/span>\r\n
\r\n
\r\n
\r\n\"\"\r\n<\/span><\/figure>\r\n
Figure <\/span>9.1<\/span> You can use a hypothesis test to decide if a dog breeder\u2019s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)<\/span><\/div>\r\n<\/div>\r\n
\r\n

Chapter Objectives<\/span><\/h3>\r\n<\/header>
\r\n
\r\n

By the end of this chapter, the student should be able to:<\/p>\r\n\r\n

    \r\n \t
  • Differentiate between Type I and Type II Errors<\/li>\r\n \t
  • Describe hypothesis testing in general and in practice<\/li>\r\n \t
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.<\/li>\r\n \t
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.<\/li>\r\n \t
  • Conduct and interpret hypothesis tests for a single population proportion.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><\/div>\r\n

    One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals<\/span> are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.<\/p>\r\n

    A statistician will make a decision about these claims. This process is called \"hypothesis testing<\/span>.\" A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.<\/p>\r\n

    In this chapter, you will conduct hypothesis tests on single means and single proportions.\r\nYou will also learn about the errors associated with these tests.<\/p>\r\n

    Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:<\/p>\r\n\r\n

      \r\n \t
    1. Set up two contradictory hypotheses.<\/li>\r\n \t
    2. Collect sample data (in homework problems, the data or summary statistics will be given to you).<\/li>\r\n \t
    3. Determine the correct distribution to perform the hypothesis test.<\/li>\r\n \t
    4. Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.<\/li>\r\n \t
    5. Make a decision and write a meaningful conclusion.<\/li>\r\n<\/ol>\r\n\r\n\r\n<\/div>","rendered":"


      \n[latexpage]
      \n<\/span><\/p>\n

      \n
      \n

      \n\"\"
      \n<\/span><\/figure>\n
      Figure <\/span>9.1<\/span> You can use a hypothesis test to decide if a dog breeder\u2019s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)<\/span><\/div>\n<\/div>\n
      \n
      \n

      Chapter Objectives<\/span><\/h3>\n<\/header>\n
      \n
      \n

      By the end of this chapter, the student should be able to:<\/p>\n

        \n
      • Differentiate between Type I and Type II Errors<\/li>\n
      • Describe hypothesis testing in general and in practice<\/li>\n
      • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.<\/li>\n
      • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.<\/li>\n
      • Conduct and interpret hypothesis tests for a single population proportion.<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<\/div>\n

        One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals<\/span> are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.<\/p>\n

        A statistician will make a decision about these claims. This process is called “hypothesis testing<\/span>.” A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.<\/p>\n

        In this chapter, you will conduct hypothesis tests on single means and single proportions.
        \nYou will also learn about the errors associated with these tests.<\/p>\n

        Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:<\/p>\n

          \n
        1. Set up two contradictory hypotheses.<\/li>\n
        2. Collect sample data (in homework problems, the data or summary statistics will be given to you).<\/li>\n
        3. Determine the correct distribution to perform the hypothesis test.<\/li>\n
        4. Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.<\/li>\n
        5. Make a decision and write a meaningful conclusion.<\/li>\n<\/ol>\n

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