# 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?

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.

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.

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?

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

What is the p-value ?

What is your decision regarding null hypothesis. Explain why?

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?

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

What is the p-value?

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

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?

What is the tested value? (formula value.)

What is the p-value?

What is your decision regarding null hypothesis?

Explain why?

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?

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

What is the p-value?

What is your decision regarding null hypothesis?  Explain why?

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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