Proportion

Latoya wants to estimate p = the proportion of all students at her large boarding high school that like the cafeteria's food. She interviews an SRS of 50 of the students living in the dormitory and finds that 14 think the cafeteria's food is good. Check to see if the conditions for calculating a confidence interval for p are met

(LT 7.3.1 #1)

• Random? Latoya interviews an SRS of 50 students √

  Large Counts? 50(14/50) = 14 ≥ 10 and 50(36/50) = 36 ≥10 √

• Random? Latoya interviews an SRS of 50 students √

  Large Counts? 50(14/50) = 14 < 10 and 50(36/50) = 36 < 10 √

• Fails Large Counts

• Not Random

An online retailer wants to estimate p = the proportion of all orders in a given week that are from new customers. He takes an SRS of 40 orders and finds that 12 of them are from new customers. Check to see if the conditions for calculating a confidence interval for p are met

(LT 7.3.1 #2)

• Random? The online retailer takes an SRS of 40 orders √

  Large Counts? 40(12/40) = 12 ≥ 10 and 40(28/40) = 28 ≥10 √

• Random? Latoya interviews an SRS of 50 students √

  Large Counts? 40(12/40) = 12 < 10 and 40(28/40) = 28 < 10 √

• Fails Large Counts

• Not Random

Upset with a proposal for a new law in his state, Ryan emailed his representative in the legislature to express his disapproval. The representative emailed him back saying that only 2 of the 200 messages he had received opposed the new proposed law. Check to see if the conditions for calculating a confidence interval for p are met, where p = the proportion of all registered voters in the state who oppose the proposed law.

(LT 7.3.1 #3)

• Random? Representative received 200 emails √

  Large Counts? 200(2/200) = 2 ≥ 10 and 200(198/200) = 198 ≥10 √

• Fails Random and Large Counts

• Fails Large Counts

• Not Random

The small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells. Whelks often drill into mussels, but this behavior appears to be more or less common in different locations. Researchers collected whelk eggs from the coast of Oregon, raised the whelks in the laboratory, and then put each whelk in a container with some delicious mussels. Only 9 of 98 whelks drilled into a mussel. Check to see if the conditions for calculating a confidence interval for p are met, where p = the proportion of all Oregon whelks that will spontaneously drill into mussels.

(LT 7.3.1 #4)

• Random? Collected 98 whelk eggs (not sure if random) √

  Large Counts? 98(9/98) = 9 ≥ 10 and 98(89/98) = 89 ≥10 √

• Fails Random and Large Counts

• Fails Large Counts

• Not Random

Use technology to find the critical value z* for a 98% confidence interval. Assume that the Large Counts condition is met.

(LT 7.3.2 #1)

• z* = 0.98

• z* = 0.01

• z* = -2.326

• z* = 2.326

Use technology to find the critical value z* for a 93% confidence interval. Assume that the Large Counts condition is met.

(LT 7.3.2 #2)

• z* = 0.93

• z* = 0.035

• z* = -1.812

• z* = 1.812

Use technology to find the critical value z* for a 75% confidence interval. Assume that the Large Counts condition is met.

(LT 7.3.2 #3)

• z* = 0.75

• z* = 0.125

• z* = -1.150

• z* = 1.150

Use technology to find the critical value z* for a 99.9% confidence interval. Assume that the Large Counts condition is met.

(LT 7.3.2 #4)

• z* = 0.999

• z* = 0.0005

• z* = -3.291

• z* = 3.291

Latoya wants to estimate p = the proportion of all students at her large boarding high school that like the cafeteria's food. She interviews an SRS of 50 of the students living in the dormitory and finds that 14 think the cafeteria's food is good. Calculate a 90% confidence interval for the proportion of students at Latoya's school who like the cafeteria's food.

(LT 7.3.3 #1)

• 0.176 to 0.384

• 0.28 to 0.104

• 0.28 - 0.104

• 0.28 + 0.104

An online retailer wants to estimate p = the proportion of all orders in a given week that are from new customers. He takes an SRS of 40 orders and finds that 12 of them are from new customers. Calculate a 99% confidence interval for the proportion of the week's orders that are from new customers.

(LT 7.3.3 #2)

• 0.113 to 0.487

• 0.30 to 0.187

• 0.30 + 0.187

• 0.30 - 0.187