STAT 200 Week 6 Homework Problems 9.1.2 Many high school s ✓ Solved

Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.

Is there enough evidence to show that the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in Pennsylvania is more than the proportion in Utah? Test at the 1% level.

Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level.

Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level.

Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level.

Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level.

Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.

Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas.

Do the data show that there is a difference between some of the suppliers? Test at the 1% level.

Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level.

Paper For Above Instructions

Introduction

This paper presents an analysis of several statistical questions concerning various groups and measurements. The focus includes the proportion of female students taking AP exams, the prevalence of Autism Spectrum Disorder (ASD) in urban versus rural areas, price comparisons between two wholesale fish companies, traffic counts on specific dates, mean income comparisons between genders, total brain volume in schizophrenia patients, and confidence intervals for various statistical questions.

Analysis of Female Students Taking AP Exams

To estimate the difference in the proportion of female students taking the biology exam versus the calculus AB exam, we use the data from 2007 where 84,199 females took the biology exam out of 144,796 total students, and 102,598 females took the calculus AB exam out of 211,693 students.

The proportion of females in biology is 0.5813 and in calculus AB is 0.4847. The difference in proportions can be calculated as follows:

Difference = p1 - p2 = 0.5813 - 0.4847 = 0.0966.

To find a 90% confidence interval for this difference, we calculate the standard error and utilize the z-score for the 90% confidence level (1.645). The confidence interval is calculated as:

CI = (0.0966 - 1.645 SE, 0.0966 + 1.645 SE).

ASD Prevalence Comparison

In Pennsylvania, there are 245 diagnosed eight-year-olds out of 18,440 evaluated, while in Utah, there are 45 diagnosed out of 2,123 evaluated. The proportions are 0.0133 for Pennsylvania and 0.0212 for Utah. Using a hypothesis test at the 1% significance level, we set up:

Null Hypothesis (H0): pPA ≤ pUT

Alternative Hypothesis (Ha): pPA > pUT

Using a Z-test for proportions, we calculate the test statistic and compare the p-value against 0.01 to draw a conclusion.

Price Comparison Between Fish Wholesalers

To determine if prices are significantly different between All Fresh Seafood and Catalina Offshore Products, we utilize a two-sample t-test at a 5% significance level. The average prices of fish types from both wholesalers are compared based on the data provided. The null hypothesis asserts that there is no price difference.

Traffic Count Analysis

Estimating the mean difference in traffic counts between the 6th and the 13th using paired data involves computing the mean for both counts and determining the confidence interval for the mean difference.

Gender Income Comparison

The income data suggests we need to verify whether males earn more than females using a one-sample t-test at a 1% significance level. The hypothesis is set as:

H0: Average male income ≤ Average female income

Ha: Average male income > Average female income

Results from the analysis lead to a p-value which will guide our decision to reject or fail to reject the null hypothesis.

Brain Volume Analysis

The total brain volumes for schizophrenia patients and normal controls will be evaluated using a t-test. Here, we will compute the averages and determine a confidence interval to establish whether schizophrenia patients have statistically lower brain volumes than normal controls under a 10% significance level.

Cell Phone Usage Comparison

The final statistical inquiry compares cell phone usage across European and American countries. A two-sample t-test will help establish if the mean number of cell phones per 100 residents is significantly different at a 98% confidence level.

Conclusion

The results of these analyses aim to provide insights into educational demographics, health disparities, economic differences, and consumer behavior through statistical methods. Further investigation and continuous monitoring of these variables can aid in addressing relevant social issues effectively.

References

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  • Autism and developmental. (2008). Retrieved from [insert source]

  • Seafood online. (2013). Retrieved from [insert source]

  • Buy sushi grade. (2013). Retrieved from [insert source]

  • Friday the 13th. (2013). Retrieved from [insert source]

  • Median income of. (2013). Retrieved from [insert source]

  • SOCR data oct2009. (2013). Retrieved from [insert source]

  • Population reference bureau. (2013). Retrieved from [insert source]

  • Waste run up. (2013). Retrieved from [insert source]

  • Calories datafile. (2013). Retrieved from [insert source]