Blog

As 2-year-old Brianna passes a mirror, she notices that she has a milk moustache and quickly uses her sleeve to wipe it off. It is clear that Brianna knows that it is herself in the mirror. This knowledge of oneself is called

Three-year-old Devin believes that when he puts on his Spiderman costume, he becomes Spiderman. One day, dressed as Spiderman, Devin leaped into the air from his dresser. This stunt landed him in the hospital with a concussion. According to Piaget, Devin is focusing on only one aspect of a problem and ignoring other key aspects of the problem; he is engaging in

Danny is fussy when he sees the small amount of ice cream in the big bowl. To him, it doesn’t seem like enough ice cream. His mother transfers the ice cream to a smaller bowl and Danny is now satisfied. This represents __________, a critical characteristic of the preoperational period.

Please note that this question consists of seven parts. Show all your work. You may use Minitab but you need to show the steps to get the answer. Just giving the answer without showing work may result in zero for the question.  A random sample of 300 students is taken and whether the student is in Honor Roll or not and whether the student is a Music student or not are noted. A contingency table of the data is given below. Expected counts are provided within the parentheses. Music Student Honor Roll Student Total Yes No Yes 17 (16.17)   33 (33.83)   50 No 80 (80.83) 170 (169.17) 250 Total 97 203 300   Write the null and alternative hypotheses to test if there is an association between “Music Student” and “Honor Roll Student.” Under the null hypothesis, how many students, who are music student and are in Honor roll, should we expect to see? Show your calculation to get this. Calculate the test statistic for the test you set up in part 1. You may use MINITAB to get the value of final test statistic. However, you need to show the mathematical calculation that resulted in the final answer.  Under the null hypothesis, what is the distribution of the test statistic? What is the degrees of freedom of the test statistic? Calculate the p-value for the test you formulate in part 1. Write the p value as a probability statement and then use may use software (MINITAB) or provided tables to find the numerical value of the p value.  Write the final conclusion in the context of the problem (use 5% significance level). From the methods you learnt in this class, suggest another test that would answer the same research question.     

Please note that this question consists of six parts. You need to show all mathematical calculations to get the final answer. Just giving the answer without showing work may result in zero for the question. A fourth grade class is studying the environment. One of the assignments is to grow bean plants in different soils. Tommy chose to grow his bean plants in soil found outside his classroom mixed with dryer lint. Tara chose to grow her bean plants in potting soil bought at the local nursery. Nick chose to grow his bean plants in soil from his mother’s garden. No chemicals were used on the plants, only water was used. They were grown inside the classroom next to a large window. Each child grew five plants. At the end of the growing period, each plant was measured, producing the data (in inches). Question of interest is: does it appear that the three media types, used by Tommy, Tara and Nick, in which the bean plants were grown produce the same mean height? A research group in the school has decided to use One-way ANOVA to compare the mean heights of bean plants for three different media types used by Tommy, Tara and Nick. They need help from a statistician to interpret the results. Use provided partial output to answer the following questions.   Write down the null and alternative hypotheses for testing whether or not the true mean heights of the bean plants would be the same for all three different media types used by Tommy, Tara and Nick. Define the parameters and use those defined parameters when you set up the null and alternative hypotheses. Compute the degrees of freedom missing in the ANOVA output (i.e. error degrees of freedom) Compute the sum of squares missing in the table (i.e. sum of square treatment)  Compute the F-value missing in the ANOVA output. At a 5% significant level is there sufficient evidence to claim that the true mean heights of the bean plants grown by three media used by Tommy, Tara and Nick are different for at least one type of the media? Explain your answer. The outputs for Tukey pairwise comparisons are given below. Based on the output Are the mean heights of the bean plants grown by Tara and Nick significantly different? Explain your answer. Which student seems to have used the media producing the highest mean plant height?  

Use the following five-number summary: Minimum Q1 Median Q3 Maximum 15 36.5 53 72 98 Select the correct statement.

State whether below statement is either a True or a False statement. If it is false explain why. Please note that you can say something is true if it’s always true. Tensile strength tests were carried out on two different grades of wire rod resulting in the accompanying data.  Based on our “rule of thumb”, we can use the pooled estimate of the standard error. Grade Sample size Sample mean (Kg/mm2) Sample std.dev 1064 19 108 1.3 1078 15 124 1.6    

Accounts department of an airline company claims that 2 out of 10 flights depart from a certain airport are delayed. Suppose you work for the company as a statistical consultant and want to see whether true proportion of delayed flights is different from what they claim. You randomly selected 120 flights and recorded their flight status. Out of 120 sampled flights, 18 flights were delayed. p-value of the test is  

When historians look at Japan’s religious history, which tradition is Shinto most closely compared and tied to?

How do Shinto practices like shrine visits (matsuri) and seasonal festivals continue to impact modern Japanese daily life?