P-value: 0.0098Area of the critical region: 0.01Critical value(s): ±2.326

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SUMMARY

The discussion centers on hypothesis testing using a significance level of 0.01 to evaluate the XSORT method of gender selection, where the null hypothesis (H0) states that the proportion of baby girls is 0.5, and the alternative hypothesis (H1) asserts that it is different. The test is confirmed as two-tailed with a calculated test statistic of z = 2.4, resulting in a P-value of 0.0098 and a critical region area of 0.01. The critical values for this test are ±2.326, which define the rejection region for the null hypothesis.

PREREQUISITES
  • Understanding of hypothesis testing concepts
  • Familiarity with z-scores and standard normal distribution
  • Knowledge of significance levels and critical values
  • Experience using statistical calculators, specifically the invNorm function
NEXT STEPS
  • Learn how to calculate P-values using the invNorm function in statistical calculators
  • Study the implications of two-tailed tests in hypothesis testing
  • Explore the relationship between z-scores and critical values in normal distributions
  • Investigate the XSORT method and its statistical significance in gender selection
USEFUL FOR

Statisticians, data analysts, researchers conducting hypothesis testing, and anyone interested in gender selection methodologies will benefit from this discussion.

noahpww
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Use the following information to answer the questions below: A 0.01 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is different than 0.5. Assume that sample data consist of 62 girls born in 100 births, so the sample statistic of 0.62 results in a z score that is 2.4 standard deviation above 0.

(a) State the null hypothesis H0 and the alternative hypothesis H1.(b) State the type of test: Is the test two-tailed, left-tailed, or right-tailed?

Two-tailed.

(c) What is the value of the test statistic?

Test statistic: z = 2.4

(d) Find the P-value.(e) What is the area of the critical region?(f) Find the critical value(s)?

Any help with this would be greatly appreciated!
 
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Hi noahpww!

I agree that this is a two-sided test. If we have a z-score and a two sided test, how do we find the area necessary to calculated a p-value. Remember that a p-value is equivalent to an area under the normal curve here, it's just a question of how to find that area. Any ideas? :)
 
Do I use the invNorm feature in my calculator or the P-value Method?
 
noahpww said:
Do I use the invNorm feature in my calculator or the P-value Method?

I don't use a manual calculator these days, but yes I believe that the invNorm() function will return the area to the LEFT of a z-score. So now the question is how do we use that and our z-score to find the area of this two sided test?
 

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