the mean amount of money spent per week on gas by a sample of 25 drivers was found to be $57.00 with a standard deviation of $2.36. assuming the population distribution is normally distributed construct and interpret a 90% confidence interval for the mean amount of money spent on Gas per week

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Mathematics

Madison Burch

14 January, 13:39

the mean amount of money spent per week on gas by a sample of 25 drivers was found to be $57.00 with a standard deviation of $2.36. assuming the population distribution is normally distributed construct and interpret a 90% confidence interval for the mean amount of money spent on Gas per week

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Ryan Wolfe · Answer 1

See below

Step-by-step explanation:

To construct a confidence interval we use the following formula:

ci = (sample mean) + - z * (sd) / [n^ (1/2) ]

The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the upper (1-C) / 2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C) / 2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:

ci = 57 + - 1.65 * (2.36) / [25^ (1/2) ]

ci = 57 + - 3.894* / (5) = 57 + - 0.78

ci = > (56.22, 57.78)