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Chapter 10: Q. 61 (page 658)

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

Short Answer

Expert verified

One-sample z interval for a proportion.

Step by step solution

01

Concept Information

Except for birth abnormalities, drowning kills more infants between the ages of one and four.

Drowning occurs in a matter of seconds and is frequently silent.

Anyone can drown at any time when there is access to water.

02

Explanation

One proportion: ztest/interval with one sample

There are two proportions: ztest/interval with two samples

Interval ttest/one-sample ttest/one-sample ttest/one-sample ttest/one-

Two methods are used: a two-sample ttest and an interval test.

If you wish to check for a difference, equality, increase, or reduction, use a test. If you want to estimate an interval in which the true value lies, use an interval.

Because we wish to estimate the true value of one proportion, we utilize a one-sample zinterval (percent).

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Most popular questions from this chapter

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation 0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20cups filled with the large setting. Let x1-x2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). What is the shape of the sampling distribution ofx炉1-x炉2. Why?

According to sleep researchers, if you are between the ages of 12and18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.If we are interested in whether students at this high school are getting too little sleep, which of the following represents the appropriate null and alternative hypotheses?

(a) H0:渭=7.9andHa:渭<7.9

(b) H0:渭=7.9andHa:渭鈮�7.9

(c) H0:渭=9andHa:渭鈮�9

(d)H0:渭=9andHa:渭<9

(e)H0:渭鈮�9andHa:渭鈮�9

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20cups filled with the large setting. Let x炉1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the mean and standard deviation of the sampling distribution.

Golf club repairs The Ping Company makes custom-built golf clubs and competes in the $4billion golf equipment industry. To improve its business process, Ping decided to study the time it took to repair golf clubs sent to the company by mail. The company determined that 16%of a random sample of orders were sent back to the customers in 5days or less. Ping examined the processing of repair orders and made changes. Following the changes, 90%of a random sample of orders were completed within 5days. Assume that each of the estimated percent is based on a random sample of n orders.

(a) We used the sample data to construct two 90% confidence intervals for the proportion of orders completed within 5 days-one before and one after the changes at Ping. The two intervals are (0.858,0.942) and (0.109,0.211). Find the value of n.

(b) Explain why the interval (0.858-0.211,0.942-0.109)=(0.647,0.833) is not a 95% confidence interval for the improvement in the proportion of orders sent back to customers within 5 days following the change.

(c) Construct and interpret a correct 95% confidence interval to replace the one in part (b).

Refer exercise 35.Suppose we select independent SRSs of 25men aged 20to 34and 36boys aged 14and calculate the sample mean heights xMand xB.

(a) Describe the shape, center, and spread of the sampling distribution ofxM-xB.

(b) Find the probability of getting a difference in sample means xM-xBthat鈥檚 less than0mg/dl. Show your work.

(c) Should we be surprised if the sample mean cholesterol level for the 14-year-old boys exceeds the sample mean cholesterol level for the men? Explain.
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