Question

1. Suppose the amount of money UCLA students spend on movies during a one month period observes normal distribution. A sample is taken containing monthly movie spending in dollars for several UCLA students as 66.72, 50.23, 40.57, 45.53, 60.45, 70.85, 57.49, and 53.46. Round your numbers to two decimal places. All the calculation should be preceded with the formula used.

b. Estimate the average monthly movie spending by all UCLA students with a 95% confidence interval.

Answer #1

The computations would be made from the following table here:

X | (X - Mean(X))^2 |

66.72 | 122.2683063 |

50.23 | 29.51205625 |

40.57 | 227.7835563 |

45.53 | 102.6675563 |

60.45 | 22.92015625 |

70.85 | 230.6601563 |

57.49 | 3.33975625 |

53.46 | 4.85100625 |

445.3 |
744.00255 |

The sample mean and sample standard deviation here are computed as:

For n - 1 = 7 degrees of freedom, we have from t distribution tables here:

P( t_{7} < 2.365) = 0.975

Therefore, P( - 2.365 < t_{7} < 2.365) = 0.95

Therefore the confidence interval for population mean here is obtained as:

**This is the required 95% confidence interval
here.**

1. Suppose the amount of money UCLA students spend on movies
during a one month period observes normal distribution. A sample is
taken containing monthly movie spending in dollars for several UCLA
students as 66.72, 50.23, 40.57, 45.53, 60.45, 70.85, 57.49, and
53.46. Round your numbers to two decimal places. All the
calculation should be preceded with the formula used. a. Calculate
the sample mean, sample standard deviation, and standard
error.

1. Suppose the amount of money UCLA students spend on movies
during a one month period observes normal distribution. A sample is
taken containing monthly movie spending in dollars for several UCLA
students as 66.72, 50.23, 40.57, 45.53, 60.45, 70.85, 57.49, and
53.46. Round your numbers to two decimal places. All the
calculation should be preceded with the formula used.
c. From this sample, can we conclude that the average monthly
movie spending by UCLA students is lower than 63.45...

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