--%>
Assignment Help - homework help

State the hypotheses

At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

a) State the hypotheses.

b) What is the 95% confidence interval estimate of the population mean examination score if a

sample of 100 applications provided a sample mean 935?

c) Use the confidence interval approach to conduct a hypothesis test. What is your conclusion?

d) Assuming α = .05, conduct p-value based and critical-value based hypothesis tests. How do the results compare in all the three cases?

 

E

Expert

Verified

(a)

Null Hypothesis H0: µ =900

Alternative Hypothesis H1: µ ≠ 900

(b)

C.I for mean = [X-bar - Z*SD/  < µ < X-bar + Z*SD/  ]

                       = [935 - 1.96*180/10 < µ < 935 + 1.96*180/10]

                       = [899.72, 970.28]

(c)

900 is just within the interval at lower end, so we can't reject null hypothesis.

(d)

Z-statistic = (935-900)/180/

                   = 1.94

1.94 is neither greater than 1.96 nor smaller than -1.96 so we can not reject null hypothesis. P-value will be slightly greater than level of significance α.

 

   Related Questions in Basic Statistics

  • Q : STATISTICS Question This week you will

    This week you will analyze if women drink more sodas than men.  For the purposes of this Question, assume that in the past there has been no difference.  However, you have seen lots of women drinking sodas the past few months.  You will perform a hypothesis test to determine if women now drink more

    		•
  • Q : Regression Analysis 1. A planning

    1. A planning official in the Texas Department of Community Affairs, which works in the office next to you, has a problem. He has been handed a data set from his boss that includes the costs involved in developing local land use plans for communities wi

    		•
  • Q : Correlation analysis and the regression

    1).  When you take out a mortgage, there are many different kinds of costs.  Usually the two largest are the interest rate (annual percentage that determines the size of your monthly payment) and the loan fee (a one-time percentage charged to you at the time

    		•
  • Q : Point of estimate standing data se to

    standing data se to develop a point of estimate

    		•
  • Q : Data Description 1. If the mean number

    1. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.) A. 2.1% B. 4.5% C. 0.3% D. 4.2% 2. The probability of an offender having a s

    		•
  • Q : What is Inter-arrival times

    Inter-arrival times:A) Requests arrive randomly, often separated by small time intervals with few long separations among themB) The time until the next arrival is independent of when the last arrival occurredC) Coro

    		•
  • Q : Safety and Liveness in Model Checking

    Safety and Liveness in Model Checking Approach; •? Safety: Nothing bad happens •? Liveness: Something good happens •? Model checking is especially good at verifying safety and liveness properties    –?Concurrency i

    		•
  • Q : Calculate the p- value Medical tests

    Medical tests were conducted to learn about drug-resistant tuberculosis. Of 284 cases tested in New Jersey, 18 were found to be drug- resistant. Of 536 cases tested in Texas, 10 were found to be drugresistant. Do these data indicate that New Jersey has a statisti

    		•
  • Q : Designing a system What are the

    What are the questions that comes into mind when designing a system?

    		•
  • Q : Variance and standard error A hospital

    A hospital treated 412 skin cancer patients over a year. Of these, 197 were female. Give the point estimate of the proportion of females seeking treatment for skin cancer. Give estimates of the

    		•