A. The average number of hours worked per week for college students is 27, and the standard deviation is 6. Assume the data is normally distributed.

Determine the z-score for 35 hours.

Determine the probability of someone working at least 35 hours.

Determine the margin of error with 95% confidence if 64 people were surveyed.

Determine the 95% confidence interval.

B. A sample of 40 speedometer for “Pragia” is obtained in Tamale and each is calibrated to check for accuracy at 55kmh. The resulting sample average and sample standard deviation are 53.8 and 1.3 respectively. Does the sample information suggest that the true mean for the speedometers is not accurate at 55kmh? Use an alpha level of 0.01.

C. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006.

D. A random sample of 100 preschool children in Kadjebi revealed that only 60 had been vaccinated for Yellow Fever. Provide an approximate 95% confidence interval for the proportion vaccinated in that suburb.

E. In exploring possible sites for a convenience store in a large neighbourhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision?

F. To obtain an estimate of the proportion of ‘full time’ university students who have a part time job in excess of 20 hours per week, the student union decides to interview a random sample of full time students. They want the length of their 95% confidence interval to be no greater than 0.1. What size sample, n should be taken?

G. Assume that in a certain district the average monthly income of persons aged 20 to 40 is GHS1300.00 with a standard deviation of GHS100. A random sample of 64 persons aged 20 to 40 from village x of the same district has an average monthly income of GHS1320.00. Does the average monthly income of the dwellers of the village (aged 20 to 40) differ from that of the inhabitants of the district (aged 20 to 40) in general, at a 5% Level of significance?

Question

A. The average number of hours worked per week for college students is 27, and the standard deviation is 6. Assume the data is normally distributed.

Determine the z-score for 35 hours.
Determine the probability of someone working at least 35 hours.
Determine the margin of error with 95% confidence if 64 people were surveyed.
Determine the 95% confidence interval.

B. A sample of 40 speedometer for “Pragia” is obtained in Tamale and each is calibrated to check for accuracy at 55kmh. The resulting sample average and sample standard deviation are 53.8 and 1.3 respectively. Does the sample information suggest that the true mean for the speedometers is not accurate at 55kmh? Use an alpha level of 0.01.

C. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006.

D. A random sample of 100 preschool children in Kadjebi revealed that only 60 had been vaccinated for Yellow Fever. Provide an approximate 95% confidence interval for the proportion vaccinated in that suburb.

E. In exploring possible sites for a convenience store in a large neighbourhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision?

F. To obtain an estimate of the proportion of ‘full time’ university students who have a part time job in excess of 20 hours per week, the student union decides to interview a random sample of full time students. They want the length of their 95% confidence interval to be no greater than 0.1. What size sample, n should be taken?

G. Assume that in a certain district the average monthly income of persons aged 20 to 40 is GHS1300.00 with a standard deviation of GHS100. A random sample of 64 persons aged 20 to 40 from village x of the same district has an average monthly income of GHS1320.00. Does the average monthly income of the dwellers of the village (aged 20 to 40) differ from that of the inhabitants of the district (aged 20 to 40) in general, at a 5% Level of significance?

Accepted Answer

We have given that,
Let X be a random variable i.e. number of hours that follows normal distribution…