Statistics · Guided Practice
Descriptive Statistics
8 questions with answers and video solutions. Try each one before revealing the answer.
Calculate the proportion, as a decimal.
Answer
By calculating both proportions, compare the preference of the two groups.
Answer
Adults:
A greater proportion of teenagers chose horror, compared with .
Answer
Only proportions (or percentages) put the two groups on the same scale, so only they can be compared fairly.
David has a mean of minutes and a standard deviation of minutes.
Sarah has a mean of minutes and a standard deviation of minutes.
Compare their performance.
Answer
David's delivery times are more consistent, because his standard deviation of minutes is smaller than Sarah's minutes.
State the most appropriate measure of location and measure of spread.
Answer
(a) Calculate the mean salary.
(b) State the median salary.
(c) Explain which is the better description of a typical salary.
Answer
(b) .
(c) The median. Nine of the ten employees earn , so the mean of is higher than almost everyone actually earns.
State what this tells you about the data.
Answer
A standard deviation of zero means there is no spread at all.
You must refer to the spreadsheet file 'Q6 golf.csv' for the data, and the word processing file 'Q6 Golf Answers.docx' when answering this question.
You must complete parts (a) (i) and (c) (ii) using appropriate statistical software. You must include all output from statistical software, and your answers in the word processing file 'Q6 Golf Answers.docx'.
A golf ball manufacturing company has designed a new golf ball which is more hard-wearing. The company wants to determine whether there is a difference in the distances travelled by the current and new golf balls.
To measure the distances travelled by the current and new golf balls, a random sample of 40 of the current golf balls and a random sample of 40 of the new golf balls were subjected to distance tests using a mechanical hitting machine. Data was collected for the distances travelled (in metres) of both the current and new golf balls.
The data was found to be approximately normally distributed.
(a) (i) Generate and state appropriate measures of location and spread for the current and new golf balls.
(ii) Make two valid comparisons about the driving distances of both the current and new golf balls.
(b) State appropriate null and alternative hypotheses to determine if there is a statistically significant difference between the distances travelled by the current and new golf balls.
(c) (i) State which type of hypothesis test is appropriate to determine if there is a statistically significant difference between the distances travelled by the current and new golf balls.
(ii) Perform the hypothesis test and state the p-value.
(iii) Hence interpret the p-value, and the result of the hypothesis test, in context.
Answer
(a)(i) Current golf ball: Mean = 270.275, Standard Deviation = 8.752985. New golf ball: Mean = 267.5, Standard Deviation = 9.896904.
(a)(ii) On average, the distances travelled by the new golf ball are less. The distances travelled by the new golf ball are more varied than those travelled by the current golf ball.
(b) Null: There is no difference in the mean distances travelled by the current and the new golf balls. Alternative: There is a difference in the mean distances travelled by the current and the new golf balls.
(c)(i) (Two-sample) t-test.
(c)(ii) p-value = 0.188.
(c)(iii) The p-value is greater than 0.05 (fail to reject the null hypothesis). There is insufficient evidence to suggest there is a significant difference in the mean distances travelled by the current golf ball and the new golf ball.