Week 12, Lab 13
Deliverable for Hypothesis Tests for 2-samples
For this lab, you will be using the formulas for 2-sample Means and Proportions, and the Z score tables for one and two tails. The formulas and the table are listed at the end of this page.
Respond to all following questions
Q1. A representative survey of New York City reports on attitudes toward premarital sex by gender. Female and male respondents reported different rates of disapproval, and we want to know if those different disapproval rates are statistically significant.
Carry out a 2-sample hypothesis testing for proportions to know if female disapproval rate of 40% (N=450) is statistically different from male disapproval rate of 35% (N=417). Use an alpha level of 0.05.
Obs! Your answer should include the null hypothesis, and what the result means.
Q2. What would your answer be if the Alpha level was of 0.10?
Q3. A scale measuring satisfaction with family life has been administered to a random sample of married respondents. The sample is divided into respondents with no children (N=120) and with children (N=98). Those with no children reported an average satisfaction score of 14.5, with a standard deviation of 0.6. Those with children reported an average satisfaction score of 12.6, with a standard deviation of 0.5.
While it looks like there is a difference, is this difference statistically significant? Use an alpha level of 0.10.
Obs! Your answer should include the null hypothesis, and what the result means.
Q4. What would your answer be if the Alpha level was of 0.01?
Formula for 2-sample hypothesis test for Means
Formula for 2-sample hypothesis test for Proportions
Alpha level Z scores for One or Two tailed tests
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1) With the z-obtained being 2.5, the score falls within the critical region which therefore we can reject the null hypothesis. This thus indicates that there is a statistical difference in disapproval rates between men and women when it comes to premarital sex.
2) The z-obtained still falls within the critical region so therefore there is still a statistical difference in disapproval rates between men and women. The null is still rejected.
3) With the z-obtained score (27.14) falling in the critical zone, therefore the null hypothesis is rejected and it can be concluded that there is a statistical difference in the scores.
4) There is still a statistical difference in the scores because the z-obtained falls in the critical zone and we must reject the null hypothesis.
z is 2.5, it falls within the critical region. So the null hypothesis is rejected
the difference between rates of males and females are statistically different.
z obtained is 27.14. Therefore the null hypothesis is rejected and it is also statistically different
the alpha level is statistically different and The null hypothesis is rejected
Query #1: A representative survey of New York City reports on attitudes toward premarital sex by gender. Female and male respondents reported different rates of disapproval, and we want to know if those different disapproval rates are statistically significant.
Answer: The Z-obtained result of 1.50 results in an inability to reject the null hypothesis. With a 40% disapproval rate from women compared to a disapproval rate of 35% from men, we can conclude that there is no statistical difference.
Query #2: What would your answer be if the Alpha level was of 0.10?
Answer: The answer would remain the same since the Z-score of 1.5 continues to fall outside of the critical region, irrespective of an Alpha level of 0.10.
Query #3: A scale measuring satisfaction with family life has been administered to a random sample of married respondents. The sample is divided into respondents with no children (N=120) and with children (N=98). Those with no children reported an average satisfaction score of 14.5, with a standard deviation of 0.6. Those with children reported an average satisfaction score of 12.6, with a standard deviation of 0.5.
While it looks like there is a difference, is this difference statistically significant? Use an alpha level of 0.10.
Obs! Your answer should include the null hypothesis, and what the result means.
Answer: The Z-obtained is 27.14; this results in a rejection of the null hypothesis because the Z-obtained value lies within the critical region. This means that the difference in the mean satisfaction score of persons with children is statistically significant in comparison to those without children.
Query #4: What would your answer be if the Alpha level was of 0.01?
Answer: The answer would remain unchanged because the Z-obtained is very large and rests within the critical region.
1. z obtained is 2.5, it falls within the critical region therefore the null hypothesis is rejected
2. the difference between rates of males and females are statistically different.
3. z obtained is 27.14, so we can reject the null hypothesis, and it is statistically different.
4.the alpha level also is statistically different, falls within the critical region, and the null hypothesis is rejected
1. With a Z obtained value of 1.5, there is not enough evidence to reject the null hypothesis. While there is a difference, we cannot say the difference is statistically significant. This concludes that female disapproval rate of 40% is not statistically different from male disapproval rate of 35%.
2. The answer would not change because the value 1.5 still falls outside of critical region even with Alpha of 0.10.
3. Z obtained= 27.14
The null hypothesis is rejected because Z obtained value falls inside the critical region, which means the difference in the average satisfaction score of those with children is statistically significant compared to those without children.
4. The answer would still be the same since the Z obtained value is significantly large and falls inside the critical region.
1) Z obtained = 1.5. It falls within the critical region, therefore we can reject the null hypothesis.
2) If the alpha level was 0.10, Z obtained would be outside the critical region we fail to reject the null hypothesis it is not statistically different.
3) Z obtain = 27.14 it falls within the critical region. We can reject the null hypothesis. It is statistically different.
4) With an alpha level of 0.10, it also falls within the critical region, therefore we can reject the null hypothesis it is statistically different.
1. The Z (obtained) is 2.5 which means that the Z (obtained) did fall in the critical region and for that the null hypothesis is rejected.
2. My answer would be that there is dissimilarity shown in rates between man and woman and are statistically unlike.
3. Since the Z (obtained) falls in the critical region and its seen that the null hypothesis is rejected than its statistically unlike.
4. My answer shows that it is statistically unlike according to the Z (obtained) which had fell in the critical region.
1) z-(obtained)= 2.5.
the z obtained lands on the critical region therefore the null hypothesis is rejected. the difference in rates between female and male are statistically different.
2) the difference in rates between female and male are still statistically different.
3) z= 27.14
the z obtained lands on the critical region therefore the null hypothesis is rejected therefore it is statistically different
4) it is still statistically different because the z obtained lands on the z critical region