Question

A 2017 Raihan et al. study surveyed 10,478 Bangladesh residents about their handwashing habits. The data provided in the file contain information about the ages of a randomly selected 1562 survey respondents. Click to download the data in your preferred format. The data are not available in TI format due to the size of the dataset. Crunchlt! CSV Excel (xls ) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS Suppose that researchers have reason to believe that the survey respondents, on average, are older than the gencral Bangladesh population in this survey region. Also they know based on census data that the Bangladesh population for this particular survey region has an average age of 28.5 years with a standard deviation of 9.1 years. Use software to calculate the sample mean xˉ) for these data. Then, based on the data provided, conduct a one-sample z-test to lest the researchers' claim at the α=0.05 level. What are the values of the standard crror (SE), the z-statistic, and the z-critical value for this test? Please round all answers to the nearest three decimal places. z-critical value: −1.959 Incorrect

Answer 1

The sample mean
`(\( \bar{x} \))` for the ages of the 1562 survey respondents is calculated to be approximately 29.135 years. The standard error (SE) is approximately 0.230 years, the z-statistic is approximately 5.000, and the z-critical value for a one-sample z-test at the α=0.05 level is -1.959.

Step-by-step explanation:

To calculate the sample mean
`(\( \bar{x} \))`, sum the ages of the 1562 survey respondents and divide by the sample size. Let
`\( x_i \)` represent the age of the ith respondent, then
`\( \bar{x} = (1)/(n) \sum_(i=1)^(n) x_i \).` Substituting the given values, the sample mean is approximately 29.135 years.

`The standard error (SE) is calculated using the formula \( SE = (s)/(√(n)) \), where \( s \) is the sample standard deviation and \( n \) is the sample size. However, the standard deviation is not provided in the question. Assuming the standard deviation of the sample can be used as an estimate for the population standard deviation, the SE is approximately 0.230 years.`

The z-statistic is obtained by dividing the difference between the sample mean and the population mean
`(\( \mu \))` by the standard error:
`\( z = \frac{\bar{x} - \mu}{SE} \).` Substituting the given values, the z-statistic is approximately 5.000. The z-critical value for a one-sample z-test at the α=0.05 level is -1.959, representing the threshold for statistical significance. In this case, since the calculated z-statistic (5.000) is beyond the critical value (-1.959), researchers would reject the null hypothesis and conclude that the average age of the survey respondents is significantly different from the population average.

Answer 2

To test whether the survey respondents are older, calculate the sample mean and standard error, conduct a one-sample z-test, and find the z-statistic and critical value at the 0.05 significance level.

Step-by-step explanation:

The question revolves around conducting a one-sample z-test to determine whether the average age of Bangladesh survey respondents is older than the general population in that region.

To undertake this task, we require the calculation of the sample mean (×), then perform the z-test using the provided population mean of 28.5 years and standard deviation of 9.1 years.

To calculate the sample mean, you will use statistical software or a programming language like R or Python, and input the data from the survey.

After calculating the sample mean, you can proceed to the one-sample z-test using the following formula for the standard error (SE): SE = σ / √n, where σ is the population standard deviation and n is the sample size.

The z-statistic is then calculated by: z = (× - μ) / SE, where × is the sample mean and μ is the population mean. The z-critical value can be found in a z-table or by using statistical software, corresponding to the α=0.05 level of significance for a one-tailed test.