Statistics and Probability Answers

The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?

Fifteen pupils from school B have mean IQ of 110 and a variance of 64, while 20 pupils from school C show a mean IQ of 114 and a variance of 78. What is the z-computed value?

Given the population 1,2,3,5,7,11 and 13 compute the following.

A.population of mean

B.Population of variance

C.population standard deviation

1) The researcher wants to estimate the number of hours that 5-year old children spend watching television. A sample of 50 five-year old children was observed to have a mean viewing time of 3 hours. The population is normally distributed with a population standard deviation 0.5 hour, find:

a) the best point estimate of the population mean.

b) the 90% confidence interval of the population mean.

2) The mean scores of a random sample of 17 students who took a special test is 83.5. If the sd of the scores is 4.1, the sample comes from an approximately normal population, find the point and interval estimates of the population mean adopting a confidence level of 95%.

3) In a gymnasium, physical exercise has a mean length of 30 mins with a sd of 6 mins. A PE major wants to estimate the true length of the exercise with a maximum error pegged at 0.5 adopting the 95% confidence interval. How many respondents does he need?

3) A social worker reports that 30% of workers in a factory are below 15 years of age. Of the 120 employees surveyed, 38 said they were below 15 years old. Using ? = 0.05, interpret the p-value.

2) A politician claims that she will receive 60% of the votes in the upcoming election. Of a random sample of 200 voters, there were 100 who will surely vote for her. Test the politician’s assertion at the 0.05 level of significance.

A school administrator claims that less than 50% of the students of the school are dissatisfied

by the community cafeteria service. Test this claim by using sample data obtained from a survey of

500 students of the school where 54% indicated their dissatisfaction of the community cafeteria

service. Use 𝐠= 0.05.

1) Complete the table.

n X p₀ z p-value

a) 120 21 5%

b) 138 32 7%

c) 200 45 10%

d) 392 102 18%

e) 612 236 20%

f) 100 40 8%

g) 248 51 10%

h) 312 100 12%

1) If a hypothesis is conducted using 𝐠= 0.05, for which of the following p-values would the null hypothesis be rejected?

2) For each pair of ? and p-value, indicate whether the null hypothesis would be rejected.

3) In a test of H₀: µ = 80 against H₁: µ＜80, the sample data yielded the test statistic z = 1.63. What is

the p-value for the test?

4) In a test of H₀: µ = 80 against H₁: µ ≠ 80, a sample of observations had a mean and standard

deviation s = 4.1. What is the p-value for this test?

5) In a test of H₀: µ = 72 against H₁: µ ≠ 72, the sample data yielded the test statistic z = 1.63. Find the p-value for the test.

Drinking water has become an important concern among people. The quality of drinking water

must be monitored as often as possible during the day for possible contamination. Another variable of

concern is the pH level, which measures the alkalinity or the acidity of the water. A pH below 7.0 is

acidic while a pH above 7.0 is alkaline. A pH of 7.0 is neutral. A water-treatment plant has a target pH

of 8.0. Based on 16 random water samples, the mean and the standard deviation were found to be: X¯= 7.6 s = 0.4

Does the sample mean provide enough evidence that it differs significantly from the target

mean? In other words, does the sample come from a population whose mean is the same as the

target pH of ? Use , two-tailed test.

1.    Assuming that the samples come from normal distributions, find the margin of error  given the following:

a. n = 10 and X = 28 with s = 4.0, 90% confidence

b. n = 16 and X = 50 with s = 4.2, 95% confidence

c. n = 20 and X = 68.2 with s = 2.5, 90% confidence

d. n = 23 and X = 80.6 with s = 3.2, 95% confidence

e. n = 25 and X = 92.8 with s = 2.6, 99% confidence

2.    Using the information in number 2, find the interval estimates of the population mean.