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

In summary, we are conducting a hypothesis test with a 0.01 significance level to determine if the proportion of baby girls is different than 0.5 when parents use the XSORT method of gender selection. The null hypothesis, H0, states that there is no difference in proportion, while the alternative hypothesis, H1, states that there is a difference. This is a two-tailed test, with a test statistic of z = 2.4. To find the p-value, we need to use the invNorm() function and consider both tails of the test. The critical value(s) can be found by using the invNorm() function and the 0.01 significance level.
  • #1
noahpww
6
0
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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  • #2
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? :)
 
  • #3
Do I use the invNorm feature in my calculator or the P-value Method?
 
  • #4
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?
 

What is a p-value?

A p-value is a statistical measure that represents the probability of obtaining results as extreme or more extreme than the observed results, assuming the null hypothesis is true.

What does a p-value of 0.0098 mean?

A p-value of 0.0098 means that there is a 0.98% chance of obtaining results as extreme or more extreme than the observed results, assuming the null hypothesis is true.

What is the critical region?

The critical region is the range of values that would lead to rejecting the null hypothesis. In other words, if the test statistic falls within this region, it is unlikely to have occurred by chance and the null hypothesis is rejected.

What is the area of the critical region?

The area of the critical region is the probability of obtaining a test statistic that falls within that region, assuming the null hypothesis is true. In this case, the area of the critical region is 0.01 or 1%.

What are the critical values?

The critical values are the values on the test statistic that separate the critical region from the non-critical region. In this case, the critical values are ±2.326, which corresponds to a p-value of 0.01.

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