The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans. (a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (b) Provide an interpretation of the confidence interval in part (a). (1mark) (c) Conduct an appropriate hypothesis test, at the 1% level of significance to test the claim that more than 30% of all university students have student loans. Provide the hypothesis statement Calculate the test statistic value Determine the probability value

The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans.

(a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans (2 marks)

(b) Provide an interpretation of the confidence interval in part (a). (1mark)

(c) Conduct an appropriate hypothesis test, at the 5% level of significance to test the claim that more than 30% of all university students have student loans.

1. Provide the hypothesis statement
2. Calculate the test statistic value
3. Determine the probability value

2) Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 107 with a standard deviation of 6, suggesting that the average IQ is lower than she thought. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01.

a) Write the appropriate hypotheses. Be sure to define any variables you introduce.

b) Find the P-value. Use your calculator.

c) State your conclusions.

According to a report, the proportion of Lancaster University students who reported insufficient rest or sleep during each of the preceding 30 days is

8.0%, while this proportion is 8.8% for University of Cumbria students. These data are based on simple random samples of 11,545 Lancaster and 4,691 Cumbria students.

(a) Calculate a 95% confidence interval for the difference between the proportions of Lancaster and Cumbria students who are sleep deprived and interpret it in the context of the data.

(b) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two Universities. (Reminder: Check conditions.)

(c) It is possible the conclusion of the test in part (b) is incorrect. If this is the case, what type of error was made?

A recent national survey found that high school students watched an average (mean) of 6.6 DVDs per month with a population standard deviation of 0.90 hour. The distribution of DVDs watched per month follows the normal distribution. A random sample of 43 college students revealed that the mean number of DVDs watched last month was 6.10. At the 0.05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

Reject H₀ if z > -1.645

Reject H₁ if z < -1.645

Reject H₀ if z < -1.645

Reject H₁ if z > -1.645

The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans.

(a) Construct a 95% confidence interval for estimating the true proportion of all university students who have student loans

(b) Provide an interpretation of the confidence interval in part (a). (1mark)

(c) Conduct an appropriate hypothesis test, at the 5% level of significance to test the claim that more than 30% of all university students have student loans.

1. Provide the hypothesis statement
2. Calculate the test statistic value
3. Determine the probability value

1. ) Suppose College male students’ heights are normally distributed with a mean of µ = 69.5 inches and a standard deviation of σ =2.8 inches.

1. What is the probability that randomly selected male is at least 70.5 inches tall?
2. If one male student is randomly selected, find the probability that his height is less than 65.2 inches or greater than 71.2 inches.
3. How tall is Shivam if only 30.5% of students are taller than him
4. There are 30.5% of all students between Mike’s height and 75 inches. How tall is Mike?
5. If 25 male students are randomly selected, find the probability that they have a mean height no higher than 70.2 inches.

The table below shows the number of students in each year at a certain university:

Year of study 1 2 3 4 5 6 7

No. of students 300 280 275 175 92 48 30

You would like to select a random sample of 100 students from this university.

i. Explain how you would choose a simple random sample.

ii. Explain how you would choose a sample using systematic (interval) sampling method.

iii. If you use stratified sampling method to choose a sample, explain how this could be done and how many students from each year group are to be chosen for the sample.

There are three levels (levels 1 – 3) of assessment that a student must pass to complete an external course. From previous information, out of 1,000 students who undertook the course, the failures were 150 at level 1; 300 at level 2; and 120 at level 3. To be awarded a degree, students’ needs to pass all three levels. To be awarded a diploma, a student must pass at least 2 levels. Students who can pass only 1 level gets a certificate.

if they want to get the number of students that can get a certificate to 500, what should be the total intake for the course.