Exam 9: Estimating the Value of a Parameter

How much money does the average professional hockey fan spend on food at a single hockey game? Thatquestion was posed to 10 randomly selected hockey fans. The sampled results show that sample mean andstandard deviation were $19.00 and $2.6, respectively. Use this information to create a 95% confidence interval for the mean. Express the answer in the form $x \pm t / \alpha / 2 ( \mathrm {~s} / \sqrt { n } )$ .

True or False: Every Studentʹs t-distribution with n $< \mathrm { N } _ { , }$ n the number in the sample and N the number in thepopulation, will be less peaked and have thinner tails.

A student randomly selects 10 paperbacks at a store. The mean price is $8.75 with a standard deviation of $1.50.Construct a 95% confidence interval for the population standard deviation, σ. Assume the data are normallydistributed.

A confidence interval for $\mathrm { p }$ can be constructed using

The grade point averages for 10 randomly selected students in an algebra class with 125 students are listedbelow. What is the effect on the width of the confidence interval if the sample size is increased to 20?2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A sample of 25 randomly English majors has a mean test score of 81.5 with a standard deviation of10.2. Round to the nearest hundredth.

A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items thatare outdated. They will randomly sample among its 100,000 items in order to determine the proportion ofmerchandise that is outdated. The current owners have never determined their outdated percentage and cannot help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 95%confident that the margin of error is within 3%?

To select the correct Studentʹs t-distribution requires knowing the degrees of freedom. How many degrees offreedom are there for a sample of size n?

A researcher wishes to estimate the number of households with two computers. How large a sample is neededin order to be 98% confident that the sample proportion will not differ from the true proportion by more than2%? A previous study indicates that the proportion of households with two computers is 20%.

A marketing research company needs to estimate which of two medical plans its employees prefer. A randomsample of n employees produced the following 98% confidence interval for the proportion of employees whoprefer plan A: (0.241, 0.561). Identify the point estimate for estimating the true proportion of employees whoprefer that plan.

True or False? When choosing the sample size for estimating a population proportion p to within E units withconfidence $( 1 - \alpha ) 100 \% \text {, if you take } p \approx 0.5$ as the approximation to p, you will always obtain a sample size thatis at least as large as required.

Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will ofa minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of guncontrol legislation. How many citizens would need to be sampled if a 99% confidence interval was desired toestimate the true proportion to within 1%?

A pollster wishes to estimate the number of left-handed scientists. How large a sample is needed in order to be95% confident that the sample proportion will not differ from the true proportion by more than 6%? A previousstudy indicates that the proportion of left-handed scientists is 9%.

A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student wasasked, ʺAre you planning or not planning to pursue a graduate degree?ʺ Of the 1010 surveyed, 658 stated thatthey were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for theproportion of college seniors who are planning to pursue a graduate degree.

The grade point averages for 10 randomly selected junior college students are listed below. Assume the gradepoint averages are normally distributed. Find a 98% confidence interval for the true mean. Round to the nearesthundredth.2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

True or False: The chi-square distribution is a symmetric distribution is negative when the degrees of freedombecome large.

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A sample of 20 part-time workers had mean annual earnings of $3120 with a standard deviationof $677. Round to the nearest dollar.

A local bank needs information concerning the savings account balances of its customers. A random sample of15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98%confidence interval for the true mean. Assume that the account balances are normally distributed. Round to thenearest cent.