Confidence Intervals with Means Week 2

A random sample of 500 army recruits has a mean height of 68 inches with a standard deviation of 2.5 inches. If a 95% confidence interval is constructed, with all the conditions having been met, what is the margin of error?

• 68

• 6.02

• .22

• .184

Tags

CCSS.HSS.IC.B.4

The Central Limit Theorem states that:

• When the population distribution is normal, the sampling distribution will also be normal.

• the t statistic is the distance from $\overline{x}$ to $\mu$ .

• There are many t-distribution curves, but only one standard normal curve.
  
  

• When n is sufficiently large $\left(n\ge30\right)$ , the sampling distribution of $\overline{x}$ is approximately normal, even if the population distribution is not normal.

Which of the following sample sizes would the create a sampling distribution of $\overline{x}$ that is approximately normal in shape given that the population is skewed right?

•  $n=4$  

•  $n=10$  

•  $n=25$  

•  $n=60$  

In order to estimate how many pairs of shoes, on average, female teens own, a random sample of 15 female students were selected at a large high school. The number of pairs of shoes owned by each is recorded in the table below. You want to compute a 90% confidence interval for the average number of pairs of shoes owned by female students at this high school.

          25,      43,       41,       26,       36,       34,       58,       49,
          16,      52,       38,       21,       27,       42,       31

Which box plot below matches this data?

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Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

Jill works at a large veterinarian clinic. She computed a confidence interval to estimate the average yearly cost of medical care for a dog. She was 95% confident that the population mean of the yearly cost of medical care for a dog at this clinic is between $144.90 and $152.96. What was her point estimate for her confidence interval?

• $144.90

• $152.96

• $150.76

• $148.93

Tags

CCSS.HSS.IC.B.4

Given a confidence interval of (3.035, 6.465), what is the margin of error?

• 1.715

• 4.850

• 5.030

• 3.035

Tags

CCSS.6.SP.B.5C

A random sample of 14 members of a tennis club were asked how many days per week they used the club. The average number of days members used the club each week was 5 and the standard deviation was 1.716 days. Assuming all conditions have been met, compute a 99% confidence interval for the mean number of days per week members use the club.

• (4.009, 5.991)

• (4.188, 5.812)

• (3.619, 6.382)

• (3.284, 6.716)

Tags

CCSS.HSS.IC.B.4

A manufacturer constructs a 95% confidence interval for the average weight of the items he produces. The resulting interval is wider than he would like. If the manufacturer wants to increase the confidence level, how would this affect the width of the confidence interval?

• The width would decrease

• The width would increase

• This impossible to determine without more information.

• The width would not change

In order for the sampling distribution of sample means to be approximately normal, which of the following must be true?

          I. The sample size must be large ( $n\ge30$  ).
         II. The population is normally distributed.
        

• Either I or II

• I only

• II only

• Both I and II

Which boxplot would indicate that conditions have not been met to perform a confidence interval?

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