A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the taro samples are Independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.

a. Test the claim that the two samples are from populations with the same mean

What are the null and alternative hypotheses?

A.  

     

 

B.  

      

 

C.  

      

 

D.  

      

The test statistic, t, is ____. (Round to two decimal places as needed.)

The P-value is ____

(Round to three decimal places as needed.)

A poll of 1052 Americans showed that 47.4% of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.

Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses.

: p ____   ____

: p ____   ____

(Type integers or decimals. Do not round.)

Identify the test statistic.

z = ____

(Round to two decimal places as needed.)

Identify the P-value.

P-value = ____

(Round to three decimal places as needed.)

State the conclusion about the null hypothesis, as well as State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

____ the null hypothesis. There ____ sufficient evidence to ____ the claim that fewer than half of Americans prefer to watch the news rather  than read or listen to it.

Let us assume that from a population with mean μ=100 and standard deviation σ=15 a sample random variable of n=900 is selected.

What is the probability P(X ̅<101.1)?

What is the probability P(X ̅>101.5)?

What is the probability P(99.3<X ̅<100.5)?

• Find 80%, 85% and 99.9% confidence interval for the sample mean of a population, if we know that in a random sample of 70 people from the population, the sample mean is 60 and the standard deviation is 5.

A population variable has a distribution with mean u= 50 and variance o = 225. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. 7. How big must the sample size n be so that the standard deviation of the sample mean, , is equal to 1.4, i.e., o = 1.4? A) n= 11 B) n=161 C) n= 115