Question

suppose a random sample of 137 households in a city was selected to determine the average annual household spending on food at home for city residents. The sample results are contained in the accompanying table. Complete parts a and b below.

a. Using the sample standard deviation as an estimate for the population standard​ deviation, calculate the sample size required to estimate the true population mean to within ±25 with 90​% confidence. How many additional samples must be​ taken? The required sample size = ​(Round up to the nearest whole​ number.)

The number of additional samples required = ​(Type a whole​ number.)

b. Using the sample standard deviation as an estimate for the population standard​ deviation, calculate the sample size required to estimate the true population mean to within ±25 with 95% confidence. How many additional samples must be​ taken? The required sample size = ​(Round up to the nearest whole​ number.)

The number of additional samples required = (Type a whole​ number.)

3354.71
3356.05
3359.66
3361.93
3371.03
3373.35
3379.17
3385.93
3386.54
3386.59
3403.63
3403.92
3406.33
3407.93
3412.38
3424.34
3431.89
3435.35
3441.93
3451.66
3462.73
3468.88
3481.77
3493.92
3498.85
3510.82
3515.93
3517.79
3521.48
3524.25
3536.37
3541.73
3545.12
3555.52
3563.25
3570.95
3589.53
3593.76
3594.24
3626.87
3628.35
3655.42
3662.61
3663.29
3675.65
3688.14
3727.01
3736.53
3740.61
3775.27
3787.64
3894.02
3922.98

Answer 1

the sample standard deviation of the given data using excel is 142.567 since the sample standard deviation as an estimate for the population standard​ deviation so = 142.567

1 ) z at 90% = 1.645

Margin of error (E) = 25

= = 88

The required sample size =88

The number of additional samples required = 137-88 = 49

2 )

z at 90% = 1.96

Margin of error (E) = 25

= = 125

The required sample size =125

The number of additional samples required = 137-125= 12