Question

In: Statistics and Probability

In a survey, 39 people were asked how much they spent on their child's last birthday...

In a survey, 39 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $14.

Calculate, state, and interpret a 95% confidence interval to estimate the mean amount of money parents spend on their child's birthday gift. Round to the nearest 100th where necessary.

Expert Solution

Solution

Given that,

= 45

= 14

n = 39

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z/2* ( $\sqrt$ /n)

= 1.960 * (14 / $\sqrt$ 39 )

= 4.39

At 95% confidence interval estimate of the population mean is,

- E < < + E

45 - 4.39 < < 45 + 4.39

40.61 < < 49.39

(40.61 , 49.39)

orchestra answered 2 years ago

In a survey, 17 people were asked how much they spent on their child's last birthday...

In a survey, 17 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $34 and standard deviation of $8. Find the margin of error at a 95% confidence level. Give your answer to two decimal places.

In a survey, 14 people were asked how much they spent on their child's last birthday...

In a survey, 14 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $12. Construct a confidence interval at a 99% confidence level.

In a survey, 24 people were asked how much they spent on their child's last birthday...

In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $31 and standard deviation of $13. Construct a confidence interval at a 80% confidence level.

In a survey, 18 people were asked how much they spent on their child's last birthday...

In a survey, 18 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $33 and standard deviation of $5. Construct a confidence interval at a 95% confidence level. Give your answers to one decimal place. ±±

In a survey, 32 people were asked how much they spent on their child's last birthday...

In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly shaped as a normal curve with a mean of $39 and standard deviation of $6. Find the margin of error at a 98% confidence level.

In a survey, 25 people were asked how much they spent on their child's last birthday...

In a survey, 25 people were asked how much they spent on their child's last birthday gift. The results were roughly shaped as a normal curve with a mean of $40 and standard deviation of $6. Construct a confidence interval at a 98% confidence level. Give your answers to one decimal place. ± Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 75 cookies and finds...

In a survey, 26 people were asked how much they spent on their child's last birthday...

In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $7. Construct a confidence interval at a 90% confidence level. Give your answers to one decimal place and Interpret your confidence interval in the context of this problem.

In a survey, 20 people were asked how much they spent on their child's last birthday...

In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $37 and a standard deviation of $9. Find the margin of error at a 95% confidence level. Give your answer to two decimal places.

In a survey, 21 people were asked how much they spent on their child's last birthday...

In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $4. Find the margin of error at a 95% confidence level. Give your answer to two decimal places.

In a survey, 29 people were asked how much they spent on their child's last birthday...

In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $43 and standard deviation of $20. Construct a confidence interval at a 95% confidence level. Give your answers to one decimal place. ±