In a randomized study, mothers with low socioeconomic status were randomly assigned to receive and regularly use soft baby carriers (which promote more physical contact between the infant and the mother) or plastic infant seats (less physical contact) to carry their newborn babies Several follow up visits were conducted to measure various outcomes One of the outcomes that the researchers were interested in was the type of attachment (secure or insecure) babies form with their mothers Researchers used the Ainsworth Strange Situation (1969) procedure to determine the type of attachment babies had formed with their mothers by the age of 13 months The data from this study are presented in the two way contingency table below Soft baby carriers Plastic infant seats Total Secure attachment 35 17 52 Insecure attachment 10 28 38 Total 45 45 90 The results for 50 observations is also included in the attachment txt file Find the sample proportion of babies in the study with secure attachment In addition, find the sample proportion of babies carried in soft baby carriers with secure attachment, and the sample proportion of babies carried in plastic infant seats with secure attachment Compare these three values Perform a hypothesis test by hand (you can find the p value with software) todetermine if the proportion of babies carried in soft baby carriers with secure attachment differs from the proportion of babies carried in plastic infant seats with secure attachment Use a z testand asignificance level of 0 05 Another common statistic we could use is the chi squared statistic In fact, R uses this for its proportion hypothesis tests The chi squared statistic compares the observed number of observations in each cell of the two way table with the number we would expect to see if the null hypothesis were true We expect the probability of secure attachment to be the same for both types ofcarriers under the null hypothesis How many of the 45 infants in the soft baby carrier group do you expect to have secure attachment How many of the 45 infants in the plastic car seat group do you expect to have secure attachment How many infants in each carrier group do you expect to have insecure treatment Let O irepresent the observed count in celli, and E i represent the expected count for celli Then thechi squared test statistic is calculated as X 2 ( O i E i ) 2 E i Calculate X 2 by hand

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In a randomized study, mothers with low socioeconomic status were randomly assigned to receive and regularly use soft baby carriers (which promote more physical contact

In a randomized study, mothers with low socioeconomic status were randomly assigned to receive and regularly use soft baby carriers (which promote more physical contact between the infant and the mother) or plastic infant seats (less physical contact) to carry their newborn babies. Several follow-up visits were conducted to measure various outcomes. One of the outcomes that the researchers were interested in was the type of attachment (secure or insecure) babies form with their mothers. Researchers used the Ainsworth Strange Situation (1969) procedure to determine the type of attachment babies had formed with their mothers by the age of 13 months.

The data from this study are presented in the two-way contingency table below:

	Soft baby carriers	Plastic infant seats	Total
Secure attachment	35	17	52
Insecure attachment	10	28	38
Total	45	45	90

The results for 50 observations is also included in the attachment.txt file.

Find the sample proportion of babies in the study with secure attachment. In addition, find the sample proportion of babies carried in soft baby carriers with secure attachment, and the sample proportion of babies carried in plastic infant seats with secure attachment. Compare these three values.

Perform a hypothesis test by hand (you can find the p-value with software) todetermine if the proportion of babies carried in soft baby carriers with secure attachment differs from the proportion of babies carried in plastic infant seats with secure attachment. Use a z-testand asignificance level of 0.05.

Another common statistic we could use is thechi-squared statistic. In fact, R uses this for its proportion hypothesis tests.The chi-squared statistic compares the observed number of observations in each cell of the two-way table with the number we would expect to see if the null hypothesis were true.

We expect the probability of secure attachment to be the same for both types ofcarriers under the null hypothesis. How many of the 45 infants in the soft baby carrier group do you expect to have secure attachment? How many of the 45 infants in the plastic car seat group do you expect to have secure attachment?

How many infants in each carrier group do you expect to have insecure treatment?

LetOirepresent the observed count in celli, andEi represent the expected count for celli. Then thechi-squared test statistic is calculated as X² =(O_i -E_i)²/E_i

CalculateX²by hand.