Homework

TR or F The 95 percent confidence interval state that 95 percent of the sample means of a specified sample size selected from a population will be within plus and minus 1.96 standard  deviations of the hypothesized population mean

 

TR or F The t distribution is positively skewed.

 

TR or F The first step in testing the hypothesis is to state the decision rule

 

TR or F There is only three levels of significance that is applied to all studies involving sampling.

 

TR or F The researcher must decide on the level of significance before formulating a decision

rule.

 

 

1.A random sample of 20 group leaders, supervisors, and similar personnel revealed that on the average a person spent  6. 5 years on the job before been promoted.

The population standard deviation was 1.6 years.

Using the 98 % level of confidence, what is the confidence interval within which the population mean lies?

 

 

Answer: ________________________________

 

 

  1. 2. A laboratory tested 12 chicken eggs and found that the mean amount of cholesterol was 230 milligram with sample standard deviation 14.1 milligrams.

 

Construct a 90% of confidence interval for the mean cholesterol content of all such eggs.

 

Answer:__________________________

 

Please, interpret your resulting of confidence interval.

 

Answer:____________________________

 

  1. Many Americans think it doesn’t matter which political party controls Congress. In an associated press article it was reported that 445 individuals in a sample of 1005 U. S. adults said it wouldn’t make difference which party is in power.

 

Construct a 99 % confidence interval for the proportion of U. S. adults who believe that it wouldn’t make difference which party is in power.

 

 

Answer:___________________________________

 

 

 

 

  1. 4. A recent survey found that 64.5% of the population own their homes.

In a random sample of 150 heads of households, 100 responded that they owned  their homes.

At a= 0.04 level of significance, does that indicate a difference from the national proportion?

 

What is the null hypothesis ?  _________________

What is alternate hypothesis? ____________________________

 

Is this one-tailed  or two-tailed test?   ______________

 

What is the critical value from table?

 

Answer:______________________ _________________________

 

What is the tested value? (value obtained from formula or TI-83 or StatCrunch .)

 

Answer______________________

 

What is the p-value ?

 

Answer________________________

 

What is your decision regarding null hypothesis. Explain why?

 

Answer:______________________

 

  1. Test the claim that the population of sophomore college students has a mean grade point  average greater  than 2.25. Sample statistics include  n=160 students ,  sample mean  is 2.35, and  population standard deviation  is equal  0.60

Use a=  0.01 level of  significance.

 

What  is the null hypothesis?        __________________

What is an alternate hypothesis? ______________________

 

Is this one-tailed or two-tailed test?  _______________________

 

What is the critical value from table?

 

Answer___________________

 

What is the tested value? (value obtained from formula or TI-83 or Statcrunch.)

 

Answer_______________

 

What is the p-value?

 

Answer:_________________

 

What is your decision regarding null hypothesis. Explain why you accept or reject it

 

Answer: ____________________________

 

 

  1. 6. The average running time for current Broadway shows is 2 hours 12 minutes.

A producer in another city claims that the length of time of productions in his city is the same.

He samples 20 shows and finds the time to be 2 hours 11 minutes with a sample standard deviation of 7 minutes. Using level of significance a= 0.05, is the producer correct?

 

What  is the null hypothesis?    ________________

What is alternate hypothesis?    ________________

 

What is the critical value?

 

Answer:______________

 

What is the tested value? (formula value.)

 

Answer:_______________

 

What is the p-value?

 

Answer:_________________

 

What is your decision regarding null hypothesis?

Explain why?

 

Answer:___________________

 

  1. 7. Smoking and College Education.

One sample showed that among 780 randomly selected students who

completed four years of college 20% smoke . Use  a= 0.05 significance level to test the claim that the rate of smoking among those with four years of college is less than the 26% rate for the general population.

What is the null hypothesis? _____________________

What is the alternate hypothesis?___________________

 

Is this one-tailed  or two-tailed test?  __________________

 

What is the critical value?

 

Answer:______________________

 

What is the tested value? (value obtained from formula or TI-83.)

 

Answer:______________________

 

What is the p-value?

 

Answer:_________________

 

What is your decision regarding null hypothesis?  Explain why?

 

Answer:_______________________________________

 

 

  1. Having a sample size of n = 100 and σ= 10 population standard deviation, we test the hypothesis that the mean is equal to 100, namely H0: µ = 100. Assuming that the observations are normally distributed we found that the sample mean is 150. The [Z or t] test statistic is equal to

 

  1. 645
  2. 960
  3. 50
  4. 13

 

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