. A physician made a survey of the roundworm infection of a rural region in Hubei province in 1999. There were 68 infected among the 350 randomly sampled males, and 36 infected among the 250 females.
(1). Please make a statistical table according to the information above the material.
(2). Is female different from male for the roundworm infection rate ? Please make a statistical inference to judge.
To create a statistical table based on the given information, we can divide it into two groups: males and females. Here's how we can set up the table:
Group | Number Sampled | Number Infected
-----------------------------------------------
Males | 350 | 68
Females | 250 | 36
Now, let's analyze whether there is a difference between males and females in terms of roundworm infection rate. To do this, we can use a statistical inference test, such as the chi-square test for independence.
Step 1: Set up hypotheses
Null hypothesis (H0): There is no difference between males and females in terms of roundworm infection rate.
Alternative hypothesis (Ha): There is a difference between males and females in terms of roundworm infection rate.
Step 2: Calculate expected frequencies
To perform the chi-square test, we need to calculate the expected frequencies for each group. We can do this by multiplying the proportions of infected individuals in each group by the total number of individuals in that group.
For males:
Expected infected = (68/350) * 350 = 68
Expected non-infected = 350 - 68 = 282
For females:
Expected infected = (36/250) * 250 = 36
Expected non-infected = 250 - 36 = 214
Step 3: Calculate the chi-square test statistic
The chi-square test statistic is calculated using the formula:
χ2 = Σ( (O-E)^2 / E )
Where:
χ2 = chi-square test statistic
O = observed frequency
E = expected frequency
We can plug in the values for each group and calculate the test statistic.
χ2 = ((68-68)^2 / 68) + ((282-282)^2 / 282) + ((36-36)^2 / 36) + ((214-214)^2 / 214)
Step 4: Determine the critical value and p-value
With the calculated test statistic, we can compare it to the critical value from the chi-square distribution table with (r-1)(c-1) degrees of freedom, where r and c are the number of rows and columns, respectively.
If the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference between males and females in terms of roundworm infection rate. Moreover, we can also calculate the p-value associated with the test statistic to further determine the significance level of the results.
Step 5: Interpretation of the results
Using the critical value or the p-value, we can make a statistical inference based on the given information and the obtained test statistic.
Please note that without the p-values or critical values, it is not possible for me to draw meaningful conclusions regarding the difference between males and females in terms of roundworm infection rate. These test values are required to make a statistical inference.