9. In order to investigate a rumor that there is a greater than expected number of girls among thechildren of chemists, Science magazine conducted an informal survey of eight chemistrydepartments. A secretary in the chemistry department at Indiana University, Bloomington,thought there might be something to this rumor and made sure that every one of the 34 facultymembers in her department who have children responded to the Science survey. Altogetherthese Indiana chemists have 53 (56%) girls and 41 (44%) boys. Is this evidence that chemistsproduce more girl babies than expected? What kind of data would you prefer before drawingthis type of conclusion? Explain how your idea would make the evidence produced moreconvincing.

Question
Asked Mar 7, 2019
9. In order to investigate a rumor that there is a greater than expected number of girls among the
children of chemists, Science magazine conducted an informal survey of eight chemistry
departments. A secretary in the chemistry department at Indiana University, Bloomington,
thought there might be something to this rumor and made sure that every one of the 34 faculty
members in her department who have children responded to the Science survey. Altogether
these Indiana chemists have 53 (56%) girls and 41 (44%) boys. Is this evidence that chemists
produce more girl babies than expected? What kind of data would you prefer before drawing
this type of conclusion? Explain how your idea would make the evidence produced more
convincing.
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9. In order to investigate a rumor that there is a greater than expected number of girls among the children of chemists, Science magazine conducted an informal survey of eight chemistry departments. A secretary in the chemistry department at Indiana University, Bloomington, thought there might be something to this rumor and made sure that every one of the 34 faculty members in her department who have children responded to the Science survey. Altogether these Indiana chemists have 53 (56%) girls and 41 (44%) boys. Is this evidence that chemists produce more girl babies than expected? What kind of data would you prefer before drawing this type of conclusion? Explain how your idea would make the evidence produced more convincing.

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check_circleExpert Solution
Step 1

Hypotheses:

Denote p as the true population proportion of girl children of chemists.

The chemistry faculty members at the university serve as the sample. Among all the children of the 34 faculty members, 53 are girls and 41 are boys. So, the total number of children is 53 + 41 = 94.

The hypothesis tested using the sample observations is:

H0 : p = 0.5, that is, the true proportion of girl children of chemists is the same as that of their proportion of boy children, versus,

H1 : p > 0.5, that is, the true proportion of girl children of chemists is greater than that of their proportion of boy children.

Step 2

Test:

In order to test the hypothesis, the test for one proportion is used. The sample size of 94 being quite large, the normal approximation is used (as a rule of thumb, a sample size greater than 30 is considered large enough). Thus, the test used is the one proportion z-test. The test is conducted using MINITAB software.

Software procedure:

  • Choose Stat > Basic Statistics > 1-Proportion.
  • In Number of trials, enter the sample size of 94 and in Number of Events, enter number of observations of girl children as 53.
  • Enter Hypothesized proportion as5.
  • Select Options.
  • Choose Proportion > hypothesized proportion in Alternative hypothesis.
  • Click OK in all dialogue boxes.

The output using Minitab is given below:

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Step 3

Conclusion:

The confidence level was taken by default as 95%, implying that the level of significance, α, for the test is 5% or 0.05. Note that the p-value is 0.058.

Decision based on the p-value method:

  • If p-value < α, reject H0.
  • If p-value ≥ α, reject H0.

Here, the ...

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