40. Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. Express the answer in the form p E and round to the nearest ten-thousandth.

0.4375 0.4048

0.5625 0.4048

0.4375 0.0129

0.5625 0.0129

41. Suppose a 98% confidence interval for turns out to be (1000, 2100). If this interval was based on a sample of size n = 22, explain what assumptions are necessary for this interval to be valid.

The population of salaries must have an approximate t distribution.

The sampling distribution of the sample mean must have a normal distribution.

The population must have an approximately normal distribution.

The sampling distribution must be biased with 21 degrees of freedom.

42. A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 17 new rackets at 56 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: x = 55 psi, s = 3.5 psi. In order to conduct the test, the customer selected a significance level of ?=0.01. Interpret this value.

The smallest value of that you can use and still reject H0 is 0.01.

The probability of making a Type II error is 0.99.

The probability of concluding that the true mean is less than 56 psi when in fact it is equal to 56 psi is only .01.

There is a 1% chance that the sample will be biased.

43. The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have PC's at home. Find the rejection region for this test using ?=0.10.

Reject H0 if z > 1.645 or z < -1.645.

Reject H0 if z > 1.28.

Reject H0 if z < -1.28.

Reject H0 if z = 1.28.

44. A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $550.

Group of answer choices

0.9987

0.7857

0.2143

0.0013

45. A local retailer claims that the mean waiting time is less than 5 minutes. A random sample of 20 waiting times has a mean of 3.5 minutes with a standard deviation of 2.1 minutes. At = 0.01, test the retailer's claim. Assume the distribution is normally distributed.

(a) State the null and alternative hypothesis.

(b) Find the test statistic and round it to the nearest hundredth.

(c) Using either classical approach or p-value approach, do you reject the null hypothesis or not? Why?

(d) provide a conclusion for the test