Question

In: Statistics and Probability

there is an old wives tale that women who eat chocolate during pregnancy are more likely...

there is an old wives tale that women who eat chocolate during pregnancy are more likely to have happy babies. a pregnancy magazine wants to test this claim, and it gathers 100 randomly selected pregnant women for its study. half of the women sampled agreed to eat chocolate at least once a day, while the other half agree to forego chocolate for the duration of their pregnancies. a year later, the ladies complete a survery regarding the overall happiness of their babies. the results are given in the following table. at the 0.01 level of significance, test the old wives' tale.

	happy babies	unhappy babies
with chocolate	24	26
without chocolate	22	28

state the null and alternative hypothesis

determine which distrubition to use for the test statistic, and state level of significance

gather date and calculate the necessary sample statistics

and draw a conclusion and interpret the decision

Expert Solution

We have to perform chi square test for independence.

H₀ : The variables habit of having chocolate during pregnancy and nature of baby are independent.

H_a : The variables habit of having chocolate during pregnancy and nature of baby are dependent.

Observed frequency table :

We need to find expected frequency.

Expected frequency =

For example expected frequency for cell with chocolate and happy babies = ( 50* 46/100) = 23

Expected frequency table :

Now we need to find chi square statistic:

χ² = ; O is observed and E is expected.

χ² = 0.161

Critical value:

We are given level of significance α = 0.01

Degrees of freedom (df) = (r-1)(c-1) r is type of habits and c is number of types of nature of babies.

r = 2 and c = 2

df = (2-1)*(2-1) = 1

Therefore critical value χ²_(0.01,1) = 6.6349 -------- ( From chi square table )

Critical region : Reject H₀ if χ² is greater than χ²_(0.01,1) = 6.6349

fail to reject H₀ , if χ² is less than χ²_(0.01,1) = 6.6349

Decision : As χ² = 0.161 is less than χ²_(0.01,1) = 6.6349

We fail to reject H₀, so accept H₀

Conclusion: We do not have significant evidence that the variables habit of having chocolate during pregnancy and nature of baby are dependent ; that is they are independent.

So the women who eat chocolate during pregnancy are not more likely to have happy babies.

orchestra answered 1 year ago

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