Question

Question: The probability that a standard normal variable, Z, is below 1.96 is 0.4750. (T/F)

Question-After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95 percent confidence interval that goes from 0.36 to 0.54.

True or False: 95 percent of the people will recognize the product between 36% and 54% of the time.

Question: A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 0.59 ± 0.07. Interpret this interval.

Please provide your answer in the rich text box.

	A	We are 95 percent confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66
	B	95 percent of the students get between 52 percent and 66 percent of their tuition paid for by financial aid
	C	We are 95 percent confident that between 52 percent and 66 percent of the sampled students receive some sort of financial aid
	D	We are 95 percent confident that 59 percent of the students are on some sort of financial aid Question: Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary? Question: As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same. (T/F) Question: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.​ (T/F) Question: The mean of the sampling distribution of a sample proportion is the population proportion, π.​ (T/F) A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms. During February, a sample of 25 days has a sample mean of 370 rooms. True or False: The parameter of interest is the proportion of the rooms rented daily in a given month.​

Answer 1

(1) False

The probability that a standard normal variable, Z, is below 1.96 is 0.4750.

Reason:

Using Standard normal Z-table,

The probability that a standard normal variable, Z, is below 1.96 is 0.9750.

(2) True:

Reason:

Confidence interval means we are 95% confident that the true value of the population lies between these intervals thus, Statement is right.

95 per cent of the people will recognize the product between 36% and 54% of the time.

(3)

Option (A) is correct.

Reason:

Confidence interval means we are 95% confident that the true value of the population lies between these intervals thus, Statement is right.

(4)

Standard error =

=

=0.12