Suppose the age of onset for Parkinson's disease in the general population is known to have a mean of 68 years. A medical researcher selects a random sample of 32 Parkinson's patients of African American ethnicity and records the age of onset for each patient. He decides to use a one-sample t-test to determine whether age of onset for African Americans differs in some way from the general population, obtaining the SPSS output below. One-Sample Statistics \begin{tabular}{l|r|r|r|r} & \( N \) & Mean & Std. Deviation & Std. Error Mean \\ \hline age of onset & 32 & 67.16 & 2.604 & 460 \\ \hline \end{tabular} One-Sample Test \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & \multicolumn{7}{|c|}{ Test Value \( =68 \)} \\ \hline & \multirow[b]{2}{*}{\( t \)} & \multirow[b]{2}{*}{ df } & \multicolumn{2}{|c|}{ Significance } & \multirow{2}{*}{\begin{tabular}{c} Mean \\ Difference \end{tabular}} & \multicolumn{2}{|c|}{\begin{tabular}{l} \( 95 \% \) Confidence Interval of the \\ Difference \end{tabular}} \\ \hline & & & One-Sided p & Two-Sided p & & Lower & Upper \\ \hline age of onset & -1.833 & 31 & .038 & .076 & -844 & -1.78 & .10 \\ \hline \end{tabular} One-Sample Effect Sizes \begin{tabular}{ll|l|l|l|l|} & & & \multicolumn{2}{c}{\( 95 \% \) Confidence Interval } \\ & Standardizer \( ^{2} \) & Point Estimate & Lower & Upper \\ \hline \multirow{2}{*}{ age of onset } & Cohen's d & 2.604 & -.324 & -.677 & .034 \\ \cline { 2 - 6 } & Hedges' correction & 2.669 & -.316 & -.661 & .033 \\ \hline \end{tabular} a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation. Hedges' correction uses the sample standard deviation, plus a correction factor.
Added by Amber P.
Close
Step 1
This involves comparing a sample mean to a known population mean. Show more…
Show all steps
Your feedback will help us improve your experience
Tim Thornhill and 96 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution? (c) Find or estimate the $P$ -value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? (e) Interpret your conclusion in the context of the application. (f) Find the requested confidence interval for the population variance or population standard deviation. Interpret the results in the context of the application. Veterinary Science: Tranquilizer Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 10 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 24 minutes. At the $1 \%$ level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a $95 \%$ confidence interval for the population standard deviation.
Chi-Square and $F$ Distributions
Testing and Estimating a Single Variance or Standard Deviation
Calculate the following Confidence Intervals: STAT – Proportions/z Statistics/t Statistics – one/two sample – with summary/data. Use the Standard-Wald method. Copy and paste the StatCrunch output table. Write your Conclusion in Context. 1) A Pew Research Center poll of 1501 randomly selected US adults showed that 70% of the respondents believe in global warming. Find the 95% Confidence Interval estimate of the population proportion p. Based on the results, can we safely conclude that the majority of adults believe in global warming? Explain this answer. 2) A simple random sample of 50 adults (including males and females) is obtained, and each person’s red blood cell count (in cells per microliter) is measured. The sample mean is 4.63. The population standard deviation for red blood cell counts is 0.54. Construct a 99% Confidence Interval estimate of the mean red blood cell count of adults. The normal range of red blood cell counts for adults is given by the NIH as 4.7 to 6.1 for males and 4.3 to 5.4 for females. What does this confidence interval suggest about these normal ranges? 3) In a test of the Atkins weight loss program, 40 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 95% Confidence Interval estimate of the mean weight loss for all such subjects. Does the Atkins program appear to be effective? Is it practical? Explain. 4) Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, CA (based on data from SigAlert). This simple random sample was obtained at 3:30 PM on a weekday. The speed limit for this road is 65 mph. Use the sample data to construct a 95% Confidence Interval for the mean speed. What does this confidence interval suggest about the speed limit? 61 57 59 58 59 69 60 67 61 62 61 54
Kari H.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD