Question

In: Statistics and Probability

1. A random sample of 40 college student students shows that the score of a College...

1. A random sample of 40 college student students shows that the score of a College Statistics is normally distributed with its mean, 81 and standard deviation, 8.4. Find 99 % confidence interval estimate for the true mean.

Solutions

Expert Solution

Solution :

Given that,

= 81

s = 8.4

n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005.39 = 2.708

Margin of error = E = t/2,df * (s /n)

= 2.708 * (8.4 / 40)

= 3.6

The 99% confidence interval estimate of the population mean is,

- E < < + E

81 - 3.6 < < 81 + 3.6

77.4 < < 84.6

(77.4,84.6)  

The 99% confidence interval 77.4 to 84.6


Related Solutions

11. A random sample of 50 college student students shows that the score of a College...
11. A random sample of 50 college student students shows that the score of a College Statistics is normally distributed with its mean, 83 and standard deviation, 7.5. Find 95 % confidence interval estimate for the true mean.
9. (19) A random sample of 64 UPW college students shows that the sample mean GPA...
9. (19) A random sample of 64 UPW college students shows that the sample mean GPA is 2.82 with a standard deviation of 0.45. (a) Construct a 90% Confidence Interval for the mean GPA of all UPW students. (b) If we want to be 95% confident, and we want to control the maximum error of estimation to 0.1, how many more students should be added into the given sample? (c) Would you conclude that the mean GPA in UPW is...
A student is interested in the sleep quality of students. That student selects a random sample...
A student is interested in the sleep quality of students. That student selects a random sample of 21 students (age 19-24 years) from each four undergraduate years (Freshman, Sophomore, Junior and Senior), and applies Pittsburgh Sleep Quality Index (PSQI) and obtains their responses. PSQI includes 19 self-reported items and is designed to evaluate overall sleep quality (Data are presented in Table 1 below). The student is interested in determining whether there is any evidence of a difference in sleep quality...
1. In a random sample of 86 college students has a mean earnings of $3120 with...
1. In a random sample of 86 college students has a mean earnings of $3120 with a standard deviation of $677 over the summer months. Determine whether a normal distribution (Z values) or a t- distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expense is normally shaped. a. Use a t distribution b. Use a normal distribution (Z values) c. Neither a normal distribution nor...
In a local university, 40% of the students live in the dormitories. A random sample of...
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is Select one: a. 0.0336 b. 0.9664 c. 0.9328 d. 0.4664
It is known that​ 35% of students change their major in college. In a random sample...
It is known that​ 35% of students change their major in college. In a random sample of 500​ students, what is the probability that less than​ 36% of these students will change their ​major? A. 0.6808 B. 0.3192 C. 0.0176 D. 0.2000
A random sample of 134 students has a test score average of 78 with a standard...
A random sample of 134 students has a test score average of 78 with a standard deviation of 10.4. Find the margin of error if the confidence level is 0.99. (Round answer to two decimal places)
In a simple random sample of 51 community college statistics students, the mean number of college...
In a simple random sample of 51 community college statistics students, the mean number of college credits completed was x=50.2 with standard deviation s = 8.3. Construct a 98% confidence interval for the mean number of college credits completed by community college statistics students. Verify that conditions have been satisfied: Simple random sample?                            n > 30? Find the appropriate critical value Since σ is unknown, use the student t distribution to find the critical value tα2 on table A-3 Degrees...
Suppose that past history shows that 5% of college students are sports fans. A sample of...
Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected. Find the probability that exactly one student is a sports fan. Find the probability that at least one student is sports fan. Find the probability that less than one student is a sports fan. Find the probability that at most one student is a sports fan. Find the probability that more than one student is a sports fan....
A random sample of 40 students has a mean annual earnings of $3120
A random sample of 40 students has a mean annual earnings of $3120. Assume the population standard deviation, σ, is $677. (Section 6.1) • Construct a 95% confidence interval for the population mean annual earnings of students.  Margin of error, E._______  Confidence interval: _______ <μ< _______ • If the number of students sampled was reduced to 25 and the level of confidence remained at 95%, what would be the new error margin and confidence interval? Margin of error, E._______  Confidence interval: _______ <μ< _______ • Did the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT